Amrit Subedi

Background: There are various approaches of modeling on time series data. Most of the studies conducted regarding time series data are based on annual trend whereas very few concerned with data having monthly fluctuation. The data of tourist arrivals is an example of time series data with monthly fluctuation which reveals that there is higher number of tourist arrivals in some months/seasons whereas others have less number. Starting from January, it makes a complete cycle in every 12 months with 3 bends indicating that it can be captured by biquadratic function.Objective: To provide an alternative approach of modeling i.e. combination of Autoregressive model with polynomial (biquadratic) function on time series data with monthly/seasonal fluctuation and compare its adequacy with widely used cyclic autoregressive model i.e. AR (12).Materials and Methods: This study is based on monthly data of tourist arrivals in Nepal. Firstly, usual time series model AR (12) has been adopted and an alternative approach of modeling has been attempted combining AR and biquadratic function. The first part of the model i.e. AR represents annual trend whereas biquadratic part does for monthly fluctuation.Results: The fitted cyclic autoregressive model on monthly data of tourist arrivals is Est. Ym = 3614.33 + 0.9509Ym-12, (R2=0.80); Est. Ym indicates predicted tourist arrivals for mth month and Ym-12 indicates observed tourist arrivals in (m-12)th month and the combined model of AR and biquadratic function is Est. Yt(m) = -46464.6 + 1.000Yt-1 + 52911.56m - 17177m2 + 2043.95m3 - 79.43m4, (R2=0.78); Est. Yt(m) indicates predicted tourist arrivals for mth month of tth year and Yt-1 indicates average tourist arrivals in (t-1)th year. The AR model combined with polynomial function reveals normal and homoscedastic residuals more accurately compared to first one.Conclusion: The use of polynomial function combined with autoregressive model can be useful for time series data having seasonal fluctuation. It can be an alternative approach for picking up a good model for such type of data. Nepalese Journal of Statistics, 2017,  Vol. 1, 41-54