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Best SARMA Models for Various Time Series 

Best SARMA Models for Various Time Series 

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In this article we are interested in the time series modeling of the average monthly maximum temperature data in Jordan. For this data, we will fit the traditional seasonal ARIMA model. Then, following McLeod (1993), we test for periodic autocorrelations among residuals of this model. We then fit a periodic autoregressive model to this time series....

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Citations

... The technique was applied to monthly flow data for the Fraser River in British Columbia and it was found that the statistical analysis of the PARMA model residuals, including a truncated Pareto model for the extreme tails produced a realistic simulation of these river flows. Smadi (2009) investigated the best of the traditional SARMA model and the relatively new PAR model for modeling the average monthly maximum temperature data in Jordan. He found that the PAR model does a better job but the fact that large number of parameters is involved, especially for monthly data, remained its main drawback. ...
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The solar radiation data taken from 14 meteorological stations in Nigeria has been analyzed. The periodic component of the data which covered a period of 13 (mostly 1977-1989) years was removed via Fourier analysis while the residual series was subjected to autoregressive analysis. It was evident from the t-test and autocorrelation plots of the modified (i.e. without the periodic component) series that there exist significant persistence at nine stations including Sokoto, Nguru, Kano, Maiduguri, Bauchi, Yola, Minna, Ibadan, and Benin. The autocorrelation at Jos, Bida, Ikeja, Enugu and Port Harcourt were however found to be insignificant. As the sample partial autocorrelation function cuts off after lag 1, a non-seasonal autoregressive model of order 1, AR (1), was identified for stations with autocorrelation. The Q-statistic of error series suggested that the models were adequate as identified. Moreover, the exploratory plots of the model residual series showed agreement with the quantitative statistics and thus enforces the inference that the models were adequate for monthly mean daily global solar radiation forecasts at some of the study stations. It is interesting to note that all the stations within the sub-sahelian region showed significant persistence whereas all the stations in the coastal region except Benin were found with insignificant autocorrelation. Expectedly, the performance evaluation of the model gave impressive result for the stations within the sub-sahelian region but a relatively weak result for the coastal region. The result for the midland region was mixed whereas it was difficult to conclude on the Guinea savannah region with result from only one station.
... Some of the time series studies are related to Jahanbakhsh and Basseri (2003) [5] research that used the mean monthly temperature of Tabriz station based on Box & Jenkins ARIMA model to examine the monthly temperature of Tabriz for a 40 year statistical period (1959-98) based on autocorrelation and partial autocorrelation methods as well as controlling the normality of residues. Smadi (2009) [2] research was based on time series modeling of the average monthly maximum temperature data in Jordan. They fitted the traditional seasonal ARIMA model. ...
... Some of the time series studies are related to Jahanbakhsh and Basseri (2003) [5] research that used the mean monthly temperature of Tabriz station based on Box & Jenkins ARIMA model to examine the monthly temperature of Tabriz for a 40 year statistical period (1959-98) based on autocorrelation and partial autocorrelation methods as well as controlling the normality of residues. Smadi (2009) [2] research was based on time series modeling of the average monthly maximum temperature data in Jordan. They fitted the traditional seasonal ARIMA model. ...
... , q are periodic coefficients, and ξ t is mean zero white noise with variance equal to one. The PARMA systems are widely applied in modeling climatology [4,5], meteorology [24], hydrology [2,21,26,28] and economics data [7,11]. PARMA time series analysis is performed in the three main processing steps: (1) identification, (2) parameter estimation, (3) diagnostic checking. ...
... But typically the periodic mean can distort our understanding (or view) of the ran- Fig. 6 Usual ACF and PACF values of 'volumes' series together with 95% confidence intervals (top and bottom plot, respectively); think inner dotted line is 95% CI for null hypothesis ofπ(n + 1) = 0 and outer is same but Bonferonni corrected for the number of n plotted (i.e. 24) dom fluctuations, thus using data after removing periodic mean is recommended as well (see Figure 6). As a result of identification stage the orders of lags p and/or q for model of PARMA type: PARMA(p,q), PAR(p) or PMA(q), should be determined. ...
Chapter
Periodic autoregressive-moving-average models (periodic ARMA models, PARMA models) are used to model nonstationary time series with periodic structure. They are similar to ARMA except the coefficients are periodic in time with a common period. They are widely applied in climatology, hydrology, meteorology and economics data. In this paper we want to familiarize the readers with all the essential steps of PARMA model fitting. We present in detail the non-parametric spectral analysis, model identification, parameter estimation, diagnostic checking (model verification) and prediction on the real data example. Our aim is to provide appropriate tool for the complete analysis of periodic time series using PARMA modeling and to popularize this approach among nonspecialists