dion11235 / time-series

Forecasting NO₂ emission Rate with SARIMA and predicting the autocorrelation with State-wise GDP

What is Seasonality?

Seasonality is a characteristic of a time series in which the data experiences regular and predictable changes that recur every calendar year. Any predictable fluctuation or pattern that recurs or repeats over a one-year period is said to be seasonal.Seasonal effects are different from cyclical effects, as seasonal cycles are observed within one calendar year, while cyclical effects, such as boosted sales due to low unemployment rates, can span time periods shorter or longer than one calendar year.

Let's look at our Data

We have have the monthly NO₂ emission rate data from January, 2005 to December ,2019 of 29 Indian states and below is the sample from Karnataka State .

As we can see , there is a prominent seasonality in the data and it is expected as NO₂ emission is mainly caused by chemical industries and that can fluctuate between months. So we are expecting a periodicity of 12 months or 1 year. Now , we are going to see a detailed description of our analysis and methodology for Karnataka state only, as we have taken the similar measures for other states also except some parameter tuning. Later we shall look at the detailed results for all the states.

Why not ARIMA and what is SARIMA ?

Autoregressive Integrated Moving Average, or ARIMA, is a forecasting method for univariate time series data.As its name suggests, it supports both an autoregressive and moving average elements. The integrated element refers to differencing allowing the method to support time series data with a trend.

A problem with ARIMA is that it does not support seasonal data. That is a time series with a repeating cycle. ARIMA expects data that is either not seasonal or has the seasonal component removed, e.g. seasonally adjusted via methods such as seasonal differencing.

Seasonal Autoregressive Integrated Moving Average, SARIMA or Seasonal ARIMA, is an extension of ARIMA that explicitly supports univariate time series data with a seasonal component.It adds three new hyperparameters to specify the autoregression (AR), differencing (I) and moving average (MA) for the seasonal component of the series, as well as an additional parameter for the period of the seasonality.