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AnalizaSzeregowCzasowych/raport/ASC.tex
Mikołaj Kaczmarek 086c1cc0a2
v1.0
2025-06-19 17:50:11 +02:00

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\documentclass[a4paper]{article}
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\lhead{Analiza Szeregów Czasowych}
\rhead{\makebox[\textwidth][r]{M. Kaczmarek, P. Wilma}}
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% Document parameters
% Document title
\title{Analiza i prognozowanie inflacji w województwach Polski}
\author{Mikołaj Kaczmarek [84985], Piotr Wilma [124832]}
\date{2025-06-19}
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\begin{document}
\maketitle
\section{Opis problemu}\label{opis-problemu}
Inflacja, rozumiana jako wzrost ogólnego poziomu cen towarów i usług w
gospodarce, to jeden z najważniejszych wskaźników makroekonomicznych. Ma
ona bezpośredni wpływ na siłę nabywczą ludności, stabilność gospodarczą
oraz decyzje inwestycyjne. Monitorowanie i prognozowanie inflacji na
poziomie województw pozwala zrozumieć zróżnicowanie procesów
gospodarczych w różnych regionach Polski, a także wspiera podejmowanie
trafnych decyzji przez samorządy, przedsiębiorców oraz mieszkańców.
Prognozy inflacji są wykorzystywane m.in. w planowaniu budżetów,
indeksacji wynagrodzeń i świadczeń, a także w ocenie ryzyka
inwestycyjnego. Aktualność i praktyczne znaczenie tego zagadnienia
sprawiają, że analiza regionalnych wskaźników inflacji stanowi
wartościowy przedmiot badań.
\subsection{Wyjaśnienie sposobu pomiaru inflacji w Banku Danych
Lokalnych}\label{wyjaux15bnienie-sposobu-pomiaru-inflacji-w-banku-danych-lokalnych}
Wskaźniki inflacji wykorzystane w niniejszej analizie pochodzą z Banku
Danych Lokalnych GUS i zostały opracowane na podstawie przeciętnych cen
producentów na rynku krajowym. Ceny skupu obejmują przeciętne roczne
ceny płacone przez podmioty gospodarcze skupujące produkty rolne
bezpośrednio od producentów rolnych. Podstawą do opracowania wskaźników
cen towarów i usług są obserwacje cen reprezentantów, a prezentowane
dane mają charakter szacunkowy.
\section{Opis sposobu
rozwiązania}\label{opis-sposobu-rozwiux105zania}
W analizie wykorzystano kwartalne dane o wskaźnikach inflacji w
poszczególnych województwach Polski z lat 2005--2024. Zbiór danych
umożliwia analizę przestrzenno-czasową oraz przygotowanie prognoz na
kolejne okresy. Zakres danych pozwala zidentyfikować trendy, sezonowość
i anomalie w kształtowaniu się inflacji regionalnej.
Dane zostały poddane oczyszczeniu oraz transformacjom przygotowującym je
do analizy szeregów czasowych. Eksploracyjna analiza danych objęła
statystyki opisowe, analizę rozkładów, wykrywanie wartości odstających
oraz identyfikację sezonowości. Do prognozowania kwartalnych wskaźników
inflacji dla każdego województwa zastosowano model ARIMA, którego
parametry zostały dobrane automatycznie na podstawie szeregów czasowych.
Podział na zbiór treningowy (do 2022 roku) oraz testowy (2023--2024)
pozwolił na ocenę jakości prognoz.
Wyniki zostały przedstawione w formie tabelarycznej oraz wizualnej
(wykresy, mapa Polski), co umożliwia intuicyjne porównanie sytuacji w
regionach oraz ocenę precyzji prognoz.
\section{Kod zawierający
obliczenia}\label{kod-zawierajux105cy-obliczenia}
Poniżej przedstawiono fragmenty kodu realizujące kolejne etapy analizy.
Po każdym bloku kodu zamieszczono odpowiadające mu wykresy oraz -- w
przypadku analizy wartości odstających -- opis procesu myślowego
dotyczącego ich interpretacji i decyzji analitycznych.
\subsection{Wczytanie i przygotowanie
danych}\label{wczytanie-i-przygotowanie-danych}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{1}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{k+kn}{import}\PY{+w}{ }\PY{n+nn}{pandas}\PY{+w}{ }\PY{k}{as}\PY{+w}{ }\PY{n+nn}{pd}
\PY{k+kn}{import}\PY{+w}{ }\PY{n+nn}{numpy}\PY{+w}{ }\PY{k}{as}\PY{+w}{ }\PY{n+nn}{np}
\PY{k+kn}{import}\PY{+w}{ }\PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot}\PY{+w}{ }\PY{k}{as}\PY{+w}{ }\PY{n+nn}{plt}
\PY{k+kn}{import}\PY{+w}{ }\PY{n+nn}{seaborn}\PY{+w}{ }\PY{k}{as}\PY{+w}{ }\PY{n+nn}{sns}
\PY{k+kn}{import}\PY{+w}{ }\PY{n+nn}{geopandas}\PY{+w}{ }\PY{k}{as}\PY{+w}{ }\PY{n+nn}{gpd}
\PY{k+kn}{from}\PY{+w}{ }\PY{n+nn}{statsmodels}\PY{n+nn}{.}\PY{n+nn}{tsa}\PY{n+nn}{.}\PY{n+nn}{arima}\PY{n+nn}{.}\PY{n+nn}{model}\PY{+w}{ }\PY{k+kn}{import} \PY{n}{ARIMA}
\PY{k+kn}{from}\PY{+w}{ }\PY{n+nn}{pmdarima}\PY{+w}{ }\PY{k+kn}{import} \PY{n}{auto\PYZus{}arima}
\PY{k+kn}{from}\PY{+w}{ }\PY{n+nn}{sklearn}\PY{n+nn}{.}\PY{n+nn}{metrics}\PY{+w}{ }\PY{k+kn}{import} \PY{n}{mean\PYZus{}absolute\PYZus{}error}
\end{Verbatim}
\end{tcolorbox}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{2}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{c+c1}{\PYZsh{} Ścieżka do pliku z danymi}
\PY{n}{data\PYZus{}path} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{raw\PYZus{}data.csv}\PY{l+s+s2}{\PYZdq{}}
\PY{c+c1}{\PYZsh{} Wczytanie i wstępna obróbka danych}
\PY{n}{df} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{read\PYZus{}csv}\PY{p}{(}\PY{n}{data\PYZus{}path}\PY{p}{,} \PY{n}{sep}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{;}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{encoding}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{utf\PYZhy{}8}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{low\PYZus{}memory}\PY{o}{=}\PY{k+kc}{False}\PY{p}{)}
\PY{n}{df}\PY{o}{.}\PY{n}{dropna}\PY{p}{(}\PY{n}{axis}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{,} \PY{n}{how}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{all}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{inplace}\PY{o}{=}\PY{k+kc}{True}\PY{p}{)}
\PY{n}{df}\PY{o}{.}\PY{n}{drop}\PY{p}{(}\PY{n}{columns}\PY{o}{=}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Atrybut}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Jednostka miary}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Kod}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wskaźnik cen}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{inplace}\PY{o}{=}\PY{k+kc}{True}\PY{p}{,} \PY{n}{errors}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ignore}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{df} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Rok}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{!=} \PY{l+m+mi}{2025}\PY{p}{]}
\PY{n}{df}\PY{o}{.}\PY{n}{rename}\PY{p}{(}\PY{n}{columns}\PY{o}{=}\PY{p}{\PYZob{}}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Nazwa}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wojewodztwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okresy}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres}\PY{l+s+s1}{\PYZsq{}}\PY{p}{\PYZcb{}}\PY{p}{,} \PY{n}{inplace}\PY{o}{=}\PY{k+kc}{True}\PY{p}{)}
\PY{n}{df}\PY{o}{.}\PY{n}{sort\PYZus{}values}\PY{p}{(}\PY{n}{by}\PY{o}{=}\PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Wojewodztwo}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Rok}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{inplace}\PY{o}{=}\PY{k+kc}{True}\PY{p}{)}
\PY{n}{df}\PY{o}{.}\PY{n}{reset\PYZus{}index}\PY{p}{(}\PY{n}{drop}\PY{o}{=}\PY{k+kc}{True}\PY{p}{,} \PY{n}{inplace}\PY{o}{=}\PY{k+kc}{True}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Rok}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Rok}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{astype}\PY{p}{(}\PY{n+nb}{int}\PY{p}{)}
\PY{n}{okres\PYZus{}mapping} \PY{o}{=} \PY{p}{\PYZob{}}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{1 kwartał}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Q1}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{2 kwartał}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Q2}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{3 kwartał}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Q3}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{4 kwartał}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Q4}\PY{l+s+s1}{\PYZsq{}}\PY{p}{\PYZcb{}}
\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{map}\PY{p}{(}\PY{n}{okres\PYZus{}mapping}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{Categorical}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{categories}\PY{o}{=}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Q1}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Q2}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Q3}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Q4}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{ordered}\PY{o}{=}\PY{k+kc}{True}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{to\PYZus{}numeric}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{str}\PY{o}{.}\PY{n}{replace}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{,}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{.}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{,} \PY{n}{errors}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{coerce}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres\PYZus{}czas}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Rok}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{astype}\PY{p}{(}\PY{n+nb}{str}\PY{p}{)} \PY{o}{+} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{str}\PY{o}{.}\PY{n}{replace}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Q}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{\PYZhy{}Q}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres\PYZus{}czas}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{PeriodIndex}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres\PYZus{}czas}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{freq}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Q}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{df} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{sort\PYZus{}values}\PY{p}{(}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wojewodztwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres\PYZus{}czas}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{reset\PYZus{}index}\PY{p}{(}\PY{n}{drop}\PY{o}{=}\PY{k+kc}{True}\PY{p}{)}
\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Kwartal}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Rok}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{astype}\PY{p}{(}\PY{n+nb}{str}\PY{p}{)} \PY{o}{+} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{\PYZhy{}}\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{astype}\PY{p}{(}\PY{n+nb}{str}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\subsection{Eksploracyjna analiza
danych}\label{eksploracyjna-analiza-danych}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{3}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{c+c1}{\PYZsh{} Informacje o danych}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{df}\PY{o}{.}\PY{n}{info}\PY{p}{(}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Zakres lat i unikalne jednostki}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+s2}{Zakres lat:}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Rok}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{min}\PY{p}{(}\PY{p}{)}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Rok}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{max}\PY{p}{(}\PY{p}{)}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Województwa:}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wojewodztwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{unique}\PY{p}{(}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Statystyki opisowe dla inflacji}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+s2}{Statystyki opisowe dla inflacji:}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{describe}\PY{p}{(}\PY{p}{)}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+s2}{Statystyki opisowe dla inflacji (grupowane według województw):}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{df}\PY{o}{.}\PY{n}{groupby}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wojewodztwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{agg}\PY{p}{(}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{mean}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{std}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{min}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{max}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\begin{Verbatim}[commandchars=\\\{\}]
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1280 entries, 0 to 1279
Data columns (total 6 columns):
\# Column Non-Null Count Dtype
--- ------ -------------- -----
0 Wojewodztwo 1280 non-null object
1 Okres 1280 non-null category
2 Rok 1280 non-null int64
3 Wartosc 1280 non-null float64
4 Okres\_czas 1280 non-null period[Q-DEC]
5 Kwartal 1280 non-null object
dtypes: category(1), float64(1), int64(1), object(2), period[Q-DEC](1)
memory usage: 51.6+ KB
None
Zakres lat: 2005 - 2024
Województwa: ['DOLNOŚLĄSKIE' 'KUJAWSKO-POMORSKIE' 'LUBELSKIE' 'LUBUSKIE'
'MAZOWIECKIE'
'MAŁOPOLSKIE' 'OPOLSKIE' 'PODKARPACKIE' 'PODLASKIE' 'POMORSKIE'
'WARMIŃSKO-MAZURSKIE' 'WIELKOPOLSKIE' 'ZACHODNIOPOMORSKIE' 'ŁÓDZKIE'
'ŚLĄSKIE' 'ŚWIĘTOKRZYSKIE']
Statystyki opisowe dla inflacji:
count 1280.000000
mean 100.835703
std 1.169597
min 99.000000
25\% 100.100000
50\% 100.500000
75\% 101.400000
max 107.000000
Name: Wartosc, dtype: float64
Statystyki opisowe dla inflacji (grupowane według województw):
mean std min max
Wojewodztwo
DOLNOŚLĄSKIE 100.82375 1.116986 99.3 105.5
KUJAWSKO-POMORSKIE 100.85125 1.221432 99.3 106.6
LUBELSKIE 100.78125 1.177757 99.1 106.3
LUBUSKIE 100.87875 1.145127 99.4 105.5
MAZOWIECKIE 100.80750 1.101986 99.3 105.3
MAŁOPOLSKIE 100.89750 1.219356 99.4 105.6
OPOLSKIE 100.83625 1.188366 99.2 105.9
PODKARPACKIE 100.85125 1.155942 99.0 104.9
PODLASKIE 100.79000 1.177704 99.3 106.7
POMORSKIE 100.80250 1.106022 99.4 105.4
WARMIŃSKO-MAZURSKIE 100.82875 1.182059 99.1 105.9
WIELKOPOLSKIE 100.88125 1.208000 99.1 106.3
ZACHODNIOPOMORSKIE 100.83125 1.152608 99.5 105.4
ŁÓDZKIE 100.85250 1.214154 99.3 106.3
ŚLĄSKIE 100.79875 1.157966 99.3 105.5
ŚWIĘTOKRZYSKIE 100.85875 1.277229 99.1 107.0
\end{Verbatim}
\emph{Wyniki: Statystyki opisowe dla inflacji w województwach}
\paragraph{Wykres: Inflacja w wybranym województwie w
czasie}\label{wykres-inflacja-w-wybranym-wojewuxf3dztwie-w-czasie}
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\prompt{In}{incolor}{4}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{c+c1}{\PYZsh{} Wykres: Inflacja w czasie dla wybranego województwa}
\PY{n}{woj} \PY{o}{=} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{WIELKOPOLSKIE}\PY{l+s+s1}{\PYZsq{}}
\PY{n}{fig}\PY{p}{,} \PY{n}{ax} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{subplots}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{16}\PY{p}{,} \PY{l+m+mi}{6}\PY{p}{)}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wojewodztwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{==} \PY{n}{woj}\PY{p}{]}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Kwartal}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{df}\PY{p}{[}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wojewodztwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{==} \PY{n}{woj}\PY{p}{]}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{marker}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{o}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+sa}{f}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Inflacja w }\PY{l+s+si}{\PYZob{}}\PY{n}{woj}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{ w czasie}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}xlabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Kwartał}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
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\PY{n}{xticks} \PY{o}{=} \PY{n}{ax}\PY{o}{.}\PY{n}{get\PYZus{}xticks}\PY{p}{(}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}xticks}\PY{p}{(}\PY{n}{xticks}\PY{p}{[}\PY{p}{:}\PY{p}{:}\PY{l+m+mi}{2}\PY{p}{]}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{setp}\PY{p}{(}\PY{n}{ax}\PY{o}{.}\PY{n}{get\PYZus{}xticklabels}\PY{p}{(}\PY{p}{)}\PY{p}{,} \PY{n}{rotation}\PY{o}{=}\PY{l+m+mi}{90}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{tight\PYZus{}layout}\PY{p}{(}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{ASC_files/ASC_7_0.png}
\end{center}
{ \hspace*{\fill} \\}
\emph{Wizualizacja: Inflacja w województwie wielkopolskim w czasie.}
\paragraph{Wykres: Porównanie rozkładów inflacji w województwach
(boxplot)}\label{wykres-poruxf3wnanie-rozkux142aduxf3w-inflacji-w-wojewuxf3dztwach-boxplot}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
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\PY{c+c1}{\PYZsh{} Wykres: Porównanie rozkładów inflacji w województwach (boxplot)}
\PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{16}\PY{p}{,}\PY{l+m+mi}{6}\PY{p}{)}\PY{p}{)}
\PY{n}{sns}\PY{o}{.}\PY{n}{boxplot}\PY{p}{(}\PY{n}{data}\PY{o}{=}\PY{n}{df}\PY{p}{,} \PY{n}{x}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wojewodztwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{y}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Rozkład inflacji w województwach}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Województwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartość}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{xticks}\PY{p}{(}\PY{n}{rotation}\PY{o}{=}\PY{l+m+mi}{90}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{tight\PYZus{}layout}\PY{p}{(}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{ASC_files/ASC_9_0.png}
\end{center}
{ \hspace*{\fill} \\}
\emph{Wizualizacja: Porównanie rozkładów inflacji w regionach --
wartości odstające są zbliżone w większości województw.}
\paragraph{Identyfikacja i analiza wartości
odstających}\label{identyfikacja-i-analiza-wartoux15bci-odstajux105cych}
W procesie eksploracji danych pojawił się problem wartości odstających
(outlierów). Wartości te mogą istotnie wpływać na wyniki modelowania
szeregów czasowych, zwłaszcza w kontekście prognozowania. Przeprowadzono
więc identyfikację wartości odstających dla każdego województwa osobno,
korzystając z klasycznej reguły pudełkowej (1.5 x IQR).
\textbf{Proces myślowy:} - Wartości odstające zostały potraktowane nie
jako anomalia danych, lecz jako potencjalny efekt rzeczywistych,
gwałtownych zmian cen wywołanych przez zjawiska o charakterze
ogólnokrajowym (np. pandemia COVID-19). - Zdecydowano się nie usuwać
outlierów, ponieważ ich obecność odzwierciedla pełną dynamikę inflacji i
pozwala modelowi ARIMA lepiej uchwycić ryzyko powtórzenia się podobnych
sytuacji w przyszłości. - Obserwacje odstające występowały w tym samym
okresie we wszystkich województwach, co sugeruje, że nie były wynikiem
błędów pomiarowych czy specyfiki regionalnej, lecz ogólnopolskich szoków
gospodarczych.
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
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\begin{Verbatim}[commandchars=\\\{\}]
\PY{k+kn}{import}\PY{+w}{ }\PY{n+nn}{warnings}
\PY{k}{def}\PY{+w}{ }\PY{n+nf}{find\PYZus{}outliers}\PY{p}{(}\PY{n}{group}\PY{p}{)}\PY{p}{:}
\PY{n}{q1} \PY{o}{=} \PY{n}{group}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{quantile}\PY{p}{(}\PY{l+m+mf}{0.25}\PY{p}{)}
\PY{n}{q3} \PY{o}{=} \PY{n}{group}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{quantile}\PY{p}{(}\PY{l+m+mf}{0.75}\PY{p}{)}
\PY{n}{iqr} \PY{o}{=} \PY{n}{q3} \PY{o}{\PYZhy{}} \PY{n}{q1}
\PY{n}{lower} \PY{o}{=} \PY{n}{q1} \PY{o}{\PYZhy{}} \PY{l+m+mf}{1.5} \PY{o}{*} \PY{n}{iqr}
\PY{n}{upper} \PY{o}{=} \PY{n}{q3} \PY{o}{+} \PY{l+m+mf}{1.5} \PY{o}{*} \PY{n}{iqr}
\PY{n}{outliers} \PY{o}{=} \PY{n}{group}\PY{p}{[}\PY{p}{(}\PY{n}{group}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{\PYZlt{}} \PY{n}{lower}\PY{p}{)} \PY{o}{|} \PY{p}{(}\PY{n}{group}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{\PYZgt{}} \PY{n}{upper}\PY{p}{)}\PY{p}{]}
\PY{k}{return} \PY{n}{outliers}
\PY{k}{with} \PY{n}{warnings}\PY{o}{.}\PY{n}{catch\PYZus{}warnings}\PY{p}{(}\PY{p}{)}\PY{p}{:}
\PY{n}{warnings}\PY{o}{.}\PY{n}{simplefilter}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ignore}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{outliers\PYZus{}df} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{groupby}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wojewodztwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{group\PYZus{}keys}\PY{o}{=}\PY{k+kc}{False}\PY{p}{)}\PY{o}{.}\PY{n}{apply}\PY{p}{(}\PY{n}{find\PYZus{}outliers}\PY{p}{)}\PY{o}{.}\PY{n}{reset\PYZus{}index}\PY{p}{(}\PY{p}{)}
\PY{n}{wojewodztwa} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wojewodztwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{unique}\PY{p}{(}\PY{p}{)}
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\PY{n}{cols} \PY{o}{=} \PY{l+m+mi}{3}
\PY{n}{rows} \PY{o}{=} \PY{p}{(}\PY{n}{n} \PY{o}{+} \PY{n}{cols} \PY{o}{\PYZhy{}} \PY{l+m+mi}{1}\PY{p}{)} \PY{o}{/}\PY{o}{/} \PY{n}{cols}
\PY{n}{fig}\PY{p}{,} \PY{n}{axes} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{subplots}\PY{p}{(}\PY{n}{rows}\PY{p}{,} \PY{n}{cols}\PY{p}{,} \PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{20}\PY{p}{,} \PY{l+m+mi}{25}\PY{p}{)}\PY{p}{,} \PY{n}{sharex}\PY{o}{=}\PY{k+kc}{False}\PY{p}{)}
\PY{n}{axes} \PY{o}{=} \PY{n}{axes}\PY{o}{.}\PY{n}{flatten}\PY{p}{(}\PY{p}{)}
\PY{k}{for} \PY{n}{i}\PY{p}{,} \PY{n}{woj} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{wojewodztwa}\PY{p}{)}\PY{p}{:}
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\PY{n}{woj\PYZus{}out} \PY{o}{=} \PY{n}{outliers\PYZus{}df}\PY{p}{[}\PY{n}{outliers\PYZus{}df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wojewodztwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{==} \PY{n}{woj}\PY{p}{]}
\PY{n}{ax} \PY{o}{=} \PY{n}{axes}\PY{p}{[}\PY{n}{i}\PY{p}{]}
\PY{n}{ax}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{woj\PYZus{}df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Kwartal}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{woj\PYZus{}df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{marker}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{o}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartości}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{scatter}\PY{p}{(}\PY{n}{woj\PYZus{}out}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Kwartal}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{woj\PYZus{}out}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{red}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Outliery}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{zorder}\PY{o}{=}\PY{l+m+mi}{5}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{n}{woj}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}xlabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Kwartal}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}ylabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{xticks} \PY{o}{=} \PY{n}{ax}\PY{o}{.}\PY{n}{get\PYZus{}xticks}\PY{p}{(}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}xticks}\PY{p}{(}\PY{n}{xticks}\PY{p}{[}\PY{p}{:}\PY{p}{:}\PY{l+m+mi}{4}\PY{p}{]}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{tick\PYZus{}params}\PY{p}{(}\PY{n}{axis}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{x}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{rotation}\PY{o}{=}\PY{l+m+mi}{90}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{8}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Ukryj puste osie}
\PY{k}{for} \PY{n}{j} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{i}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{,} \PY{n+nb}{len}\PY{p}{(}\PY{n}{axes}\PY{p}{)}\PY{p}{)}\PY{p}{:}
\PY{n}{axes}\PY{p}{[}\PY{n}{j}\PY{p}{]}\PY{o}{.}\PY{n}{set\PYZus{}visible}\PY{p}{(}\PY{k+kc}{False}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{tight\PYZus{}layout}\PY{p}{(}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{ASC_files/ASC_11_0.png}
\end{center}
{ \hspace*{\fill} \\}
\emph{Wizualizacja: Wartości odstające inflacji w poszczególnych
województwach.}
\paragraph{Wykres: Średnia inflacja w poszczególnych
kwartałach}\label{wykres-ux15brednia-inflacja-w-poszczeguxf3lnych-kwartaux142ach}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
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\PY{c+c1}{\PYZsh{} Wykres: Średnia inflacja wg kwartału}
\PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{10}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)}
\PY{n}{sns}\PY{o}{.}\PY{n}{barplot}\PY{p}{(}\PY{n}{data}\PY{o}{=}\PY{n}{df}\PY{p}{,} \PY{n}{x}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Okres}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{y}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wartosc}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
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\PY{n}{plt}\PY{o}{.}\PY{n}{ylim}\PY{p}{(}\PY{l+m+mi}{90}\PY{p}{,} \PY{k+kc}{None}\PY{p}{)}
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\PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Średnia wartość inflacji}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{tight\PYZus{}layout}\PY{p}{(}\PY{p}{)}
\PY{k}{for} \PY{n}{p} \PY{o+ow}{in} \PY{n}{plt}\PY{o}{.}\PY{n}{gca}\PY{p}{(}\PY{p}{)}\PY{o}{.}\PY{n}{patches}\PY{p}{:}
\PY{n}{plt}\PY{o}{.}\PY{n}{gca}\PY{p}{(}\PY{p}{)}\PY{o}{.}\PY{n}{annotate}\PY{p}{(}\PY{l+s+sa}{f}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+si}{\PYZob{}}\PY{n}{p}\PY{o}{.}\PY{n}{get\PYZus{}height}\PY{p}{(}\PY{p}{)}\PY{l+s+si}{:}\PY{l+s+s1}{.2f}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{p}{(}\PY{n}{p}\PY{o}{.}\PY{n}{get\PYZus{}x}\PY{p}{(}\PY{p}{)} \PY{o}{+} \PY{n}{p}\PY{o}{.}\PY{n}{get\PYZus{}width}\PY{p}{(}\PY{p}{)} \PY{o}{/} \PY{l+m+mf}{2.}\PY{p}{,} \PY{n}{p}\PY{o}{.}\PY{n}{get\PYZus{}height}\PY{p}{(}\PY{p}{)}\PY{p}{)}\PY{p}{,}
\PY{n}{ha}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{center}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{va}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{bottom}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{,} \PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{black}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{rotation}\PY{o}{=}\PY{l+m+mi}{0}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{ASC_files/ASC_13_0.png}
\end{center}
{ \hspace*{\fill} \\}
\emph{Wizualizacja: Sezonowość inflacji -- najwyższe wartości na
początku roku.}
\subsection{Prognozowanie inflacji}\label{prognozowanie-inflacji}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{8}{\boxspacing}
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\PY{k+kn}{import}\PY{+w}{ }\PY{n+nn}{warnings}
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Wojewodztwo MAE RMSE Prognoza\_nast\_Q1 \textbackslash{}
0 DOLNOŚLĄSKIE 1.057990 1.349998 103.042604
1 KUJAWSKO-POMORSKIE 1.798216 2.109858 104.257795
2 LUBELSKIE 1.842612 2.201423 104.028267
3 LUBUSKIE 2.630262 2.835831 105.125033
4 MAZOWIECKIE 2.210909 2.382601 104.222372
5 MAŁOPOLSKIE 3.100145 3.327341 104.639357
6 OPOLSKIE 1.273130 1.776170 103.269950
7 PODKARPACKIE 1.662043 1.895028 103.983461
8 PODLASKIE 1.833321 2.130977 103.564815
9 POMORSKIE 2.744541 2.935636 104.558241
10 WARMIŃSKO-MAZURSKIE 2.276361 2.514340 104.126611
11 WIELKOPOLSKIE 1.977402 2.313830 104.174993
12 ZACHODNIOPOMORSKIE 2.142560 2.486010 105.092549
13 ŁÓDZKIE 2.655085 2.851156 104.215455
14 ŚLĄSKIE 1.665346 1.921836 103.719610
15 ŚWIĘTOKRZYSKIE 1.768887 2.151510 103.898081
Prognoza\_nast\_Q2 Prognoza\_nast\_Q3 Prognoza\_nast\_Q4
0 103.757840 102.228181 101.504872
1 105.056674 103.667468 102.565568
2 104.910522 103.169437 103.041379
3 105.438958 103.761610 103.909744
4 104.959720 102.875522 103.412013
5 105.285196 104.173087 104.198731
6 103.902339 103.216132 101.984858
7 103.965890 103.159991 102.937568
8 104.852343 103.016065 102.920822
9 104.976134 103.594970 103.833097
10 104.820131 103.339697 103.488421
11 105.092403 103.631222 103.081806
12 104.985644 103.634001 103.869870
13 105.243038 103.612173 103.650360
14 104.362231 103.072617 102.792637
15 104.899030 103.249998 102.580991
\end{Verbatim}
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\emph{Wyniki: Tabela z prognozami inflacji oraz wskaźnikami jakości
prognoz (MAE, RMSE) dla każdego województwa.}
\paragraph{Wykres: Porównanie błędów prognoz MAE i
RMSE}\label{wykres-poruxf3wnanie-bux142ux119duxf3w-prognoz-mae-i-rmse}
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\begin{center}
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\end{center}
{ \hspace*{\fill} \\}
\emph{Wizualizacja: Poziom błędów prognoz w regionach.}
\paragraph{Wykres: Heatmapa prognozowanych wzrostów inflacji w kolejnych
kwartałach}\label{wykres-heatmapa-prognozowanych-wzrostuxf3w-inflacji-w-kolejnych-kwartaux142ach}
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\PY{n}{results\PYZus{}df\PYZus{}heatmap} \PY{o}{=} \PY{n}{results\PYZus{}df}
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\begin{center}
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\end{center}
{ \hspace*{\fill} \\}
\emph{Heatmapa: Prognozowane różnice inflacji w regionach w kolejnych
kwartałach.}
\subsection{Wizualizacja prognoz na mapie
Polski}\label{wizualizacja-prognoz-na-mapie-polski}
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\PY{c+c1}{\PYZsh{} Wczytaj plik geojson z granicami województw}
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\PY{c+c1}{\PYZsh{} Mapowanie nazw województw}
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\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{podlaskie}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{PODLASKIE}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}
\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{pomorskie}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{POMORSKIE}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}
\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{warmińsko\PYZhy{}mazurskie}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{WARMIŃSKO\PYZhy{}MAZURSKIE}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}
\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{wielkopolskie}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{WIELKOPOLSKIE}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}
\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{zachodniopomorskie}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ZACHODNIOPOMORSKIE}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}
\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{łódzkie}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ŁÓDZKIE}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}
\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{śląskie}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ŚLĄSKIE}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}
\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{świętokrzyskie}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ŚWIĘTOKRZYSKIE}\PY{l+s+s1}{\PYZsq{}}
\PY{p}{\PYZcb{}}
\PY{n}{gdf}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wojewodztwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{=} \PY{n}{gdf}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{nazwa}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{map}\PY{p}{(}\PY{n}{mapping}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Połącz dane z prognozą z geometrią województw}
\PY{n}{map\PYZus{}df} \PY{o}{=} \PY{n}{gdf}\PY{o}{.}\PY{n}{merge}\PY{p}{(}\PY{n}{results\PYZus{}df}\PY{p}{,} \PY{n}{on}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Wojewodztwo}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{map\PYZus{}df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Prognoza}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{=} \PY{n}{map\PYZus{}df}\PY{p}{[}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Prognoza\PYZus{}nast\PYZus{}Q1}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Prognoza\PYZus{}nast\PYZus{}Q2}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Prognoza\PYZus{}nast\PYZus{}Q3}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Prognoza\PYZus{}nast\PYZus{}Q4}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{]}\PY{o}{.}\PY{n}{mean}\PY{p}{(}\PY{n}{axis}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Wizualizacja}
\PY{n}{fig}\PY{p}{,} \PY{n}{ax} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{subplots}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{,} \PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{20}\PY{p}{,} \PY{l+m+mi}{12}\PY{p}{)}\PY{p}{)}
\PY{n}{map\PYZus{}df}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{column}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Prognoza}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{cmap}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{viridis}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{linewidth}\PY{o}{=}\PY{l+m+mf}{0.8}\PY{p}{,} \PY{n}{ax}\PY{o}{=}\PY{n}{ax}\PY{p}{,} \PY{n}{edgecolor}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{0.8}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{legend}\PY{o}{=}\PY{k+kc}{True}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Prognozowana inflacja w najbliższym kwartale (wg województw)}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{fontdict}\PY{o}{=}\PY{p}{\PYZob{}}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{fontsize}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:}\PY{l+m+mi}{16}\PY{p}{\PYZcb{}}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{axis}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{off}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Etykiety}
\PY{k}{for} \PY{n}{idx}\PY{p}{,} \PY{n}{row} \PY{o+ow}{in} \PY{n}{map\PYZus{}df}\PY{o}{.}\PY{n}{iterrows}\PY{p}{(}\PY{p}{)}\PY{p}{:}
\PY{n}{plt}\PY{o}{.}\PY{n}{annotate}\PY{p}{(}\PY{l+s+sa}{f}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+si}{\PYZob{}}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Prognoza}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{l+s+si}{:}\PY{l+s+s2}{.2f}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}
\PY{n}{xy}\PY{o}{=}\PY{p}{(}\PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{geometry}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{centroid}\PY{o}{.}\PY{n}{x}\PY{p}{,} \PY{n}{row}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{geometry}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{centroid}\PY{o}{.}\PY{n}{y}\PY{p}{)}\PY{p}{,}
\PY{n}{horizontalalignment}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{center}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{fontsize}\PY{o}{=}\PY{l+m+mi}{9}\PY{p}{)}
\PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{ASC_files/ASC_21_0.png}
\end{center}
{ \hspace*{\fill} \\}
\emph{Mapa: Prognozowane średnie wartości inflacji w nadchodzących
kwartałach.}
\begin{center}\rule{0.5\linewidth}{0.5pt}\end{center}
\section{Wyniki obliczeń}\label{wyniki-obliczeux144}
\begin{itemize}
\tightlist
\item
Dane obejmujące lata 2005--2024 wykazują umiarkowaną zmienność
wskaźnika inflacji w skali kraju i regionów, a także delikatną
sezonowość kwartalną (najwyższe wartości na początku roku).
\item
W analizowanym okresie wyraźny wzrost inflacji (lata 2021--2023) był
związany z globalnymi zjawiskami gospodarczymi (np. pandemia
COVID-19), co odnotowano we wszystkich województwach.
\item
Najtrafniejsze prognozy (najniższe MAE i RMSE) uzyskano dla województw
o stabilniejszym przebiegu inflacji (dolnośląskie, opolskie,
podkarpackie, śląskie).
\item
Największą prognozowaną dynamikę inflacji w najbliższych czterech
kwartałach odnotowano w województwach lubuskim, pomorskim, łódzkim
oraz kujawsko-pomorskim.
\item
Wyniki prognoz potwierdzają, że inflacja w Polsce ma w dużej mierze
charakter ogólnokrajowy, a różnice regionalne są stosunkowo
niewielkie.
\end{itemize}
\subsection{Podsumowanie i wnioski}\label{podsumowanie-i-wnioski}
Przeprowadzona analiza umożliwiła szczegółowe zbadanie dynamiki inflacji
w polskich województwach w latach 2005--2024 oraz opracowanie
wiarygodnych prognoz na kolejne kwartały. Dane wykazały umiarkowaną
zmienność i sezonowość wskaźnika inflacji, a także silny wpływ czynników
ogólnokrajowych na przebieg procesów inflacyjnych. Modele ARIMA
pozwoliły uzyskać dobrej jakości prognozy dla większości regionów.
Wizualizacja wyników na mapie Polski ułatwia intuicyjne porównanie
sytuacji w poszczególnych województwach.
Należy pamiętać, że prognozy opierają się na założeniu kontynuacji
dotychczasowych trendów i nie uwzględniają potencjalnych,
nieprzewidywalnych zdarzeń przyszłych. W przyszłych badaniach warto
rozważyć uwzględnienie dodatkowych zmiennych makroekonomicznych oraz
alternatywnych metod prognostycznych dla jeszcze lepszego odwzorowania
procesów inflacyjnych w Polsce.
% Add a bibliography block to the postdoc
\end{document}
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