- Moving average : Moving average is the simplest approach for modelling time series. The next data value is the average of all the previous values in the plot. Moving average models can smoothen a time series and show different trends.
- Exponential smoothing : It works on lines of moving average but with decreasing weight being assigned to each observation. Thus, less weightage is given to data values as the plot moves farther from the value being considered.
y = αxt + (1- α)y(t-1) , t>0
0< α <1 and α is the smoothing factor. It decides how fast the weight of an observation changes for previous data values. Smaller the smoothing factor, smoother is the time series.
- ARIMA ( Auto Regressive Integrated Moving Average) : ARIMA models can be used for both seasonal as well as non-seasonal time series to carry out forecasting. This method uses three variables – P, D, Q
p denotes the periods to lag for. For eg. If P=3, we will consider three previous periods of the time series as the autoregressive calculation inputs.
d refers to the number of differencing transformations to be done in a time series in order to convert a non-stationary time series into a stationary one which is done as a part of the ARIMA model of forecasting. q refers to the period of the component error, in which the component error is a part of the time series not explained by seasonality or trend.
Autocorrelation shows the relation between a time series and its past values. On the other hand, Autocorrelation function plot refers to how a time series is related with itself i.e. a plot also including the ls unit. The ACF plot is used to determine whether to use the AR term or MA term in the ARIMA model. The two are used together very rarely.
If there is a positive autocorrelation at lag 1, then the AR model is used. If there is a negative autocorrelation at lag 1, then the MA model is used. Using the Autoregressive (AR) component: A complete AR model does forecasting only while using past values similar to linear regression where AR terms used are directly proportional to the periods considered.
Using the Moving Averages (MA) component: A complete MA model smoothens the effect of sudden jumps in values of data seen in a time series plot. These jumps represent the errors calculated in the ARIMA model.
Integrated component: When the time series is non-stationary, this component is considered. The parameter for the integrated component is the number of times difference has to be taken to make the time series stationary.
Seasonal ARIMA models (Also known as SARIMA) : This model is brought into use when the time series shows seasonality. Like the ARIMA model, SARIMA model too has certain parameters. These are p,d,q, which refer to the same terms as described above in the ARIMA model. m denotes the number of periods in every season.
P,D,Q refer to p,d,q for the seasonal part of the time series.
Seasonal differencing considers the seasons and finds out the differences in the current value and the value of the same in the preceding season. For eg. differencing in the monthly sale of a certain item in December will be value in December 2019 – value in December 2018.