A deep dive into the algorithm for time series decomposition
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timeseries_decomposition.py
importpandasaspd |
importnumpyasnp |
importmath |
frommatplotlibimportpyplotasplt |
#construct the date parser |
mydateparser=lambdax: pd.datetime.strptime(x, '%d-%m-%y') |
#load the data set into a pandas data frame |
df=pd.read_csv('retail_sales_used_car_dealers_us_1992_2020.csv', header=0, index_col=0, parse_dates=['DATE'], date_parser=mydateparser) |
#plot the data set |
fig=plt.figure() |
fig.suptitle('Retail sales of used car dealers in the US in millions of dollars') |
df['Retail_Sales'].plot() |
plt.show() |
#add a column containing a 2 x 12 centered moving average. this column will capture the trend component in the time series |
df['2 x 12 CMA (TREND)'] =np.nan |
foriinrange(6,df['Retail_Sales'].size-6): |
df['2 x 12 CMA (TREND)'][i] =df['Retail_Sales'][i-6] *1.0/24+ ( |
df['Retail_Sales'][i-5] +df['Retail_Sales'][i-4] +df['Retail_Sales'][i-3] +df['Retail_Sales'][ |
i-2] +df['Retail_Sales'][i-1] +df['Retail_Sales'][i] +df['Retail_Sales'][i+1] +df['Retail_Sales'][ |
i+2] +df['Retail_Sales'][i+3] +df['Retail_Sales'][i+4] +df['Retail_Sales'][ |
i+5]) *1.0/12+df['Retail_Sales'][i+6] *1.0/24 |
#plot the trend component |
fig=plt.figure() |
fig.suptitle('TREND component of Retail sales of used car dealers in the US in millions of dollars') |
df['2 x 12 CMA (TREND)'].plot() |
plt.show() |
df['SEASONALITY AND NOISE'] =df['Retail_Sales']/df['2 x 12 CMA (TREND)'] |
#plot the seasonality and noise components |
fig=plt.figure() |
fig.suptitle('SEASONALITY and NOISE components') |
plt.ylim(0, 1.3) |
df['SEASONALITY AND NOISE'].plot() |
plt.show() |
#calculate the average seasonal component for each month |
#first add a month column |
df['MONTH'] =df.index.strftime('%m').astype(np.int) |
#initialize the month based dictionaries to store the running total of themonth wise seasonal sums and counts |
average_seasonal_values= {1:0, 2:0, 3:0, 4:0, 5:0, 6:0, 7:0, 8:0, 9:0, 10:0, 11:0, 12:0} |
average_seasonal_value_counts= {1:0, 2:0, 3:0, 4:0, 5:0, 6:0, 7:0, 8:0, 9:0, 10:0, 11:0, 12:0} |
#calculate the sums and counts |
foriinrange(0, df['SEASONALITY AND NOISE'].size): |
ifmath.isnan(df['SEASONALITY AND NOISE'][i]) isFalse: |
average_seasonal_values[df['MONTH'][i]] =average_seasonal_values[df['MONTH'][i]] +df['SEASONALITY AND NOISE'][ |
i] |
average_seasonal_value_counts[df['MONTH'][i]] =average_seasonal_value_counts[df['MONTH'][i]] +1 |
#calculate the average seasonal component for each month |
foriinrange(1, 13): |
average_seasonal_values[i] =average_seasonal_values[i] /average_seasonal_value_counts[i] |
#create a new column in the data frame and fill it with the value of the average seasonal component for the corresponding month |
df['SEASONALITY'] =np.nan |
foriinrange(0, df['SEASONALITY AND NOISE'].size): |
ifmath.isnan(df['SEASONALITY AND NOISE'][i]) isFalse: |
df['SEASONALITY'][i] =average_seasonal_values[df['MONTH'][i]] |
#plot the seasonal component |
fig=plt.figure() |
fig.suptitle('The 'Pure' SEASONAL component') |
plt.ylim(0, 1.3) |
df['SEASONALITY'].plot() |
plt.show() |
df['NOISE'] =df['SEASONALITY AND NOISE']/df['SEASONALITY'] |
#plot the seasonal component |
fig=plt.figure() |
fig.suptitle('The NOISE component') |
plt.ylim(0, 1.3) |
df['NOISE'].plot() |
plt.show() |
#Do all of the above using one line of code! |
fromstatsmodels.tsa.seasonalimportseasonal_decompose |
components=seasonal_decompose(df['Retail_Sales'], model='multiplicative') |
components.plot() |
plt.show() |
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