In this section, we will examine the Statistical Methods in time series analysis.

ARIMA:

📌 In statistics and econometrics, and in particular in time series analysis, an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. To better comprehend the data or forecast upcoming series points, both of these models are fitted to time series data. ARIMA models are applied in some cases where data show evidence of non-stationarity in the sense of mean.

ARIMA: Autoregressive + Moving Average + Trend Differencing

SARIMA:

📌 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.

SARIMA: Autoregressive + Moving Average + Trend Differencing + Seasonal Differencing

📌 Our aim here is to estimate the amount of air pollution (co2) one month later.

📌 The carbon dioxide record from Mauna Loa Observatory, known as the “Keeling Curve,” is the world’s longest unbroken record of atmospheric carbon dioxide concentrations. Scientists make atmospheric measurements in remote locations to sample air that is representative of a large volume of Earth’s atmosphere and relatively free from local influences.

Atmospheric CO2 from Continuous Air Samples at Mauna Loa Observatory, Hawaii, U.S.A. Period of Record: March 1958 - December 2001