scholarly journals A SARIMA and Adjusted SARIMA Models in a Seasonal Nonstationary Time Series; Evidence of Enugu Monthly Rainfall

2021 ◽  
Vol 2 (1) ◽  
pp. 13-18
Author(s):  
Chibuzo Gabriel Amaefula
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Diagnostic Test ◽  
Nonstationary Time Series ◽  
Stationary Time Series ◽  
Seasonal Characteristics ◽  
Parameter Redundancy ◽  
Least Squares Estimates ◽  
Underlying Variable ◽  
Sarima Models

 The paper compares SARIMA and adjusted SARIMA(ASARIMA) in a regular stationary series where the underlying variable is seasonally nonstationary.  Adopting empirical rainfall data and Box-Jenkins iterative algorithm that calculates least squares estimates, Out of 11 sub-classes of SARIMA and 7 sub-classes of ASARIMA models, AIC chose ASARIMA(2,1,1)12 over all sub-classes of SARIMA(p,0,q)x(P,1,Q)12 identified. Diagnostic test indicates absence of autocorrelation up to the 48th lag. The forecast values generated by the fitted model are closely related to the actual values. Hence, ASARIMA can be recommended for regular stationary time series with seasonal characteristics and where parameter redundancy and large sum of square errors are penalized.        

scholarly journals Non-linear time series regression

1971 ◽  
Vol 8 (04) ◽  
pp. 767-780 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Time Series ◽  
Strong Consistency ◽  
Linear Time ◽  
Stationary Time Series ◽  
Compact Set ◽  
Time Series Regression ◽  
Non Linear ◽  
Consistency And Asymptotic Normality ◽  
Image Position ◽  
Least Squares Estimates

In Jennrich (1969) the modelis considered, wherex(n) is a sequence of i.i.d. (0,σ2) random variables andz(n;θ) is a continuous but possibly non-linear function ofθ∈Θ, Θ being a compact set inRp. We shall use a second subscript when referring to a particular coordinate ofθ0so thatθ0jis thejth coordinate. Jennrich establishes, under suitable conditions onz(n;θ) andx(n), the strong consistency and asymptotic normality of the least squares estimates ofθ.Our main purpose here is to extend these results to the case wherex(n) is generated by a stationary time series.

A Moving Cross-Section Analysis of Demand for Toothpaste

1970 ◽  
Vol 7 (4) ◽  
pp. 439-449 ◽  
Author(s):  
Kristian S. Palda ◽  
Larry M. Blair
Keyword(s):  
Time Series ◽  
Panel Data ◽  
Least Squares ◽  
Cross Section ◽  
Single Equation ◽  
Cross Sectional ◽  
Least Squares Estimates ◽  
Section Analysis

MRCA panel data on toothpaste expenditures are used to demonstrate how time series and cross-sectional bias can be eliminated by the method of covariance regression from single-equation demand least squares estimates.

Point-Wise Dimension Estimate of Nonstationary, Multi-Episode, Time-Series and Application to Gearbox Signal

1999 ◽  
Author(s):  
D. C. Lin ◽  
B. J. Augustine ◽  
M. F. Golnaraghi
Keyword(s):  
Time Series ◽  
First Passage Time ◽  
Passage Time ◽  
Nonstationary Time Series ◽  
Stationary Time Series ◽  
Dimension Estimate ◽  
Estimation Algorithms ◽  
Data Segment ◽  
Multiple Episode ◽  
Autocorrelation Time

Abstract Dimensions of nonstationary time series is studied. The nonstationarity is considered to be due to multiple episode where an episode is a piece of stationary time series. The dimension estimation algorithms in the literature can be naturally extended to study multi-episode time series by restricting the calculation on data segment of pre-determined length. Inevitably, more than one episode will be included in the segment. This work focuses on finding when such dimension estimate has a local interpretation as the dimension of the episode. It was found that the local interpretation is valid if there is a large enough difference in the autocorrelation time of the episodes. This is termed EES. In practice, the average first passage time of the reconstructed “orbit” can be used to determine EES. Numerical evidence of these results are given and the application to the mechanical gearbox signal are shown.

scholarly journals Asymptotic normality of the least squares estimate in trigonometric regression with strongly dependent noise

2019 ◽  
pp. 24-41
Author(s):  
T. O. Drabyk ◽  
O. V. Ivanov
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Least Squares ◽  
Regression Function ◽  
Least Squares Estimator ◽  
Stationary Time Series ◽  
Model Parameters ◽  
Local Transformation ◽  
Stationary Time ◽  
Trigonometric Regression

The least squares estimator asymptotic properties of the parameters of trigonometric regression model with strongly dependent noise are studied. The goal of the work lies in obtaining the requirements to regression function and time series that simulates the random noise under which the least squares estimator of regression model parameters are asymptotically normal. Trigonometric regression model with discrete observation time and open convex parametric set is research object. Asymptotic normality of trigonometric regression model parameters the least squares estimator is research subject. For obtaining the thesis results complicated concepts of time series theory and time series statistics have been used, namely: local transformation of Gaussian stationary time series, stationary time series with singular spectral density, spectral measure of regression function, admissibility of singular spectral density of stationary time series in relation to this measure, expansions by Chebyshev-Hermite polynomials of the transformed Gaussian time series values and it’s covariances, central limit theorem for weighted vector sums of the values of such a local transformation and Brouwer fixed point theorem.

scholarly journals Estimation of AR (2) Model with Dependent Errors for Unbounded Stationary and Nonstationary Time Series

2021 ◽  
Vol 23 (12) ◽  
pp. 417-422
Author(s):  
Prof. Ahmed Amin EL- Sheikh ◽  
◽  
Mohammed Ahmed Farouk Ahmed ◽  
Keyword(s):  
Time Series ◽  
Sample Size ◽  
Covariance Matrix ◽  
Nonstationary Time Series ◽  
Stationary Time Series ◽  
Times Series ◽  
The Third ◽  
Stationary Conditions ◽  
Simulation Results ◽  
Better Than

In this paper the GLS and the ML estimators, the variance-covariance matrix, the unbiased for the GLS and the ML estimators of parameters of AR (2) model with constant in case of dependent errors have been derived, the simulation results shown that the values of MSE and Thiel’s U in case of unbounded stationary time series for all sample size T are less than the values of MSE and Thiel’s U in case of unbounded nonstationary time series which approved that the results for unbounded stationary times series are better than the results for unbounded nonstationary times series, and the simulation results for unbounded nonstationary time series shown that by using the measurement of MSE the best case among of all cases of nonstationary which gives the smallest values of MSE is case four when the first and the second conditions of stationary conditions for AR (2) model are exists, while by using the measurement of Thiel’s U the best case among of all cases of nonstationary which gives the smallest values of Thiel’s U is case six when the second and the third conditions of stationary conditions for AR (2) model are exists.

scholarly journals Non-linear time series regression

1971 ◽  
Vol 8 (4) ◽  
pp. 767-780 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Time Series ◽  
Strong Consistency ◽  
Linear Time ◽  
Stationary Time Series ◽  
Compact Set ◽  
Time Series Regression ◽  
Non Linear ◽  
Consistency And Asymptotic Normality ◽  
Image Position ◽  
Least Squares Estimates

In Jennrich (1969) the model is considered, where x(n) is a sequence of i.i.d. (0, σ2) random variables and z(n; θ) is a continuous but possibly non-linear function of θ∈ Θ, Θ being a compact set in Rp. We shall use a second subscript when referring to a particular coordinate of θ0 so that θ0j is the jth coordinate. Jennrich establishes, under suitable conditions on z(n; θ) and x(n), the strong consistency and asymptotic normality of the least squares estimates of θ. Our main purpose here is to extend these results to the case where x(n) is generated by a stationary time series.

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