Abstract
Periodic autoregressive moving average PARMA process extend the classical autoregressive moving average ARMA process by allowing the parameters to vary with seasons. Model identification is the identification of a possible model based on an avai lable realization, i.e., determining the type of th e model with appropriate orders. The Periodic Autocor relation Function (PeACF) and the Periodic Partial Autocorrelation Function (PePACF) serve as useful indicators of the correlation or of the dependence between the values of the series so that they play an important role in model identificatio n. The identification is based on the cut-off property of the Periodic Autocorrelation Function (PeACF). We derive an explicit expression for the asymptotic variance of the sample PeACF to be used in establishing its bands. Therefore, we will get in t his study a new structure of the periodic autocorrelation function which depends directly to the variance that will derived to be used in establishing its bands for the PMA process over the cut-off region and we have studied the theoretical side and we will apply some simulated examples with R which agrees well with the theoretical results.
Highlights
INTRODUCTIONFlows have significant periodic behavior in the mean, The time series has been found that many meteorological variables (such as rainfall, global temperature) are nonstationary
Flows have significant periodic behavior in the mean, The time series has been found that many meteorological variables are nonstationary
We will get in this study a new structure of the periodic autocorrelation function which depends directly to the variance that will derived to be used in establishing its bands for the PMA process over the cut-off region and we have studied the theoretical side and we will apply some simulated examples with R which agrees well with the theoretical results
Summary
Flows have significant periodic behavior in the mean, The time series has been found that many meteorological variables (such as rainfall, global temperature) are nonstationary. We Know that the time series analysis and modeling is an important tool in many areas in our life like water resources It is used for building mathematical models to generate synthetic hydrologic records to forecast, determine the likelihood, detect trends and shifts, and to interpolate missing data and standard deviation and skewness. In addition to these periodicities, they show a time correlation structure which may be either constant or periodic, for more details see (Anderson and Vecchia, 1993; Bartlett, 1946). We will get some properties of the variance summarized which are needed for the assessment of the cut-off property of the seasonal ACF for a season s which follows a MA(q(s)) and apply this establish on some simulated examples
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