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S. Roy and A. Chatterjee
Fig. 5.8 Seasonal decomposition results
Table 5.5 Result seasonal decomposition
Date
AQI Res AQI seas AQI
trend
Date
AQI Res
AQI seas AQI
trend
15-10-2018 −12.9174 −3.65398 109.5714 15-10-2019
7.628376 1.514481 125.8571
16-10-2018 −24.9431 1.514481 118.4286 16-10-2019 −4.16045 2.303306 130.8571
17-10-2018 23.69669 2.303306 141
17-10-2019 −37.7216
0.578711 131.1429
18-10-2018 −8.43585 0.578711 163.8571 18-10-2019
12.48609 0.228195 136.2857
5.7.2 Autoregressive Model
Here, the observations of previous steps are taken as input to an equation for forecasting the next step values. Here, the aim is to forecast value for (t + 1) when input
is for (t − 1 and t − 2).
ARIMA (Autoregressive Integrated Moving Average)
When we handle time series the ARMIA model or the autoregressive integrated
moving average model becomes a key in forecasting and predicting solutions for
problems. It is a class of statistical models. In terms of mathematics, if L be a lag
operator,
1 −
p
−d
i=1
ϕ i L
i
= (1 − L)
d