import plotly.express as pxdef cat_gdp(yearly_data):return pd.qcut(yearly_data, q=3, labels=['Developing', 'Emerging', 'Developed'])df = gapminder# Apply the function to each yeardf['GDP_Category'] = df.groupby('year').apply(lambda x: cat_gdp(x.gdpPercap)).reset_index(level=0, drop=True)df_Af = df.query("continent == 'Asia'")# Aggregate the datadf_agg = df_Af.groupby(['year', 'GDP_Category']).size().reset_index(name='Count')# Create the stacked bar chartfig = px.bar( df_agg, x='year', y='Count', color='GDP_Category', barmode='stack', title="Evolution of Asian Countries' GDP from 1952 to 2007", labels={'Count': 'Number of Countries', 'year': 'Year'})fig.update_layout(height=410, width=500)fig.show()
Visualization & Statistical values
Statistical values: Autocorrelation
We’re interested in how the current value influences the succeeding/later values?
Consider the mean temperature & its lags:
Temp
Lag1
Lag2
Lag3
0
10.000
15.833
12.250
16.667
1
15.833
12.250
16.667
15.600
2
12.250
16.667
15.600
19.000
3
16.667
15.600
19.000
22.333
4
15.600
19.000
22.333
24.143
Q1: If Temp and Lag1 are highly correlated, what does that mean?
A1:Current highly correlated with next.
Correlations of our example:
Temp
Lag1
Lag2
Lag3
Temp
1.0
0.89
0.82
0.71
Autocorrelation at lag \(\color{blue}{k}\) of \((X_t)\): \[r_{\color{blue}{k}}=\frac{n}{n-\color{blue}{k}}\frac{\sum_{t=1}^{n-\color{blue}{k}}(X_t-\overline{X})(X_{t+\color{blue}{k}}-\overline{X})}{\sum_{t=1}^{n}(X_t-\overline{X})^2},\] where \(\overline{X}=\frac{1}{n}\sum_{t=1}^nX_t\) (average).
Interpretation: for any lag \(k:-1\leq r_k\leq 1\) and it indicates the correlation between original timeseies with its \(k\)-lag timeseries.
Visualization & Statistical values
Visualization: Correlogram/ACF plot
It shows the relation between the lag \(k\) and the \(r_k\).
In python :
Code
from statsmodels.graphics.tsaplots import plot_acf_, ax = plt.subplots(2,1,figsize=(5, 3.65))plot_acf(df_lag.Temp, lags=60, ax=ax[0])ax[0].set_title('Correlogram for Mean Temperature', fontsize=13)ax[0].set_xlabel('Lag')ax[0].set_ylabel('Autocorrelation')sns.lineplot(df_climate.iloc[::12,:].iloc[:60,:], x="date", y="meantemp", ax=ax[1])ax[1].set_title("Mean temperature", fontsize=13)ax[1].set_ylabel("")ax[1].set_xlabel("")plt.xticks(df_climate.iloc[::12,:].iloc[:60,:].date[::10], rotation=45, size=8)plt.tight_layout()plt.show()
Interpretation:
The autocorrelation oscillates between 1 and -1, showing a periodic pattern of the temperature.
Peaks and troughs in autocorrelation repeat approximately every 30 lags, indicating cycles in the data.
Values outside the shaded region indicate significant autocorrelation, which points to a strong relationship between temperature at specific lags.
