Time Series Modelling of the Metheorological Parameters of Different Cities of Pakistan

Abstract

Time series modelling and forecasting hold pivotal significance in various practical domains. Forecasting deals with different applications in meteorology and environment fields and has attracted a lot of attention from various corners of the world to do active research work in this field in the last couple of years. In this regard various models have been proposed for improving the accuracy and efficiency of time series modelling and forecasting. The present investigation aims to present a main description of some popular time series forecasting models. The mean monthly data of the five stations of Pakistan: Karachi, Lahore, Peshawar, Islamabad and Quetta are selected, each station involving six parameters: Rf (precipitation), Tmin (minimum temperature), Tmax (maximum temperature), Rh (relative humidity), Ws (wind speed) and Ap (atmospheric pressure) for the period of 28 years (1990-2017). The current study deals with univariate modelling and multivariate modelling methods. The first method deals with the decomposition of time series, Auto regressive (AR) model with seasonal dummies, Autoregressive Moving average (ARMA) / Autoregressive Integrated Moving average (ARIMA) models, whereas the latter method deals with Vector Autoregressive (VAR) model and Granger Causality test. We have discussed a test for measuring the unit root identification, which is pre-requisite for these forecasting methods is Augmented Dickey Fuller (ADF) test. For checking the reliability of the forecast results i-e diagnostic checking and the residuals for the fitted model is examined through Chi-Square by means of goodness of fit test. Finally, for finding the best fitted model, the performance measures of various models: Root Mean Squire Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) were considered. The best fitted model chosen is subject to least value of performance measures, concluded AR-Model with seasonal dummies as best fitted model. In last we will forecast the monthly values for the year 2018, for selected parameters by best fitted model