Diagnostic Checking of Periodic Autoregression Models With Application

McLeod, A. Ian

doi:10.1111/j.1467-9892.1994.tb00186.x

Cited by 124 publications

(118 citation statements)

References 25 publications

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“…Notice that for Monday, the first difference is with respect to the Sunday spot price and Tuesday's first difference is with respect to the Monday price, etcetera. The reported periodic autocorrelations are computed as described in McLeod (1994). For example, the third column shows r Mon (7) = corr(∆p t , ∆p t−7 ) = 0.26.…”

Section: Time Series Descriptives Of Nord Pool Electricity Spot Pricesmentioning

confidence: 99%

Periodic Seasonal Reg-ARFIMA–GARCH Models for Daily Electricity Spot Prices

Koopman

Ooms

Carnero

2007

Journal of the American Statistical Association

222

128

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Novel periodic extensions of dynamic long memory regression models with autoregressive conditional heteroskedastic errors are considered for the analysis of daily electricity spot prices. The parameters of the model with mean and variance specifications are estimated simultaneously by the method of approximate maximum likelihood. The methods are implemented for time series of 1, 200 to 4, 400 daily price observations. Apart from persistence, heteroskedasticity and extreme observations in prices, a novel empirical finding is the importance of day-of-the-week periodicity in the autocovariance function of electricity spot prices. In particular, daily log prices from the Nord Pool power exchange of Norway are modeled effectively by our framework, which is also extended with explanatory variables. For the daily log prices of three European emerging electricity markets (EEX in Germany, Powernext in France, APX in The Netherlands), which are less persistent, periodicity is also highly significant.

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Section: Time Series Descriptives Of Nord Pool Electricity Spot Pricesmentioning

confidence: 99%

Periodic Seasonal Reg-ARFIMA–GARCH Models for Daily Electricity Spot Prices

Koopman

Ooms

Carnero

2007

Journal of the American Statistical Association

222

128

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“…It can be shown that r j (ν) are asymptotically unbiased and consistent estimators of ρ j (ν) (McLeod, 1995). As far as the PAR ω (1) is considered, it can be proved that the first lag autocorrelations are given by:…”

Section: Properties Of Ols Estimates With Correlated Errorsmentioning

confidence: 99%

“…In this article we study the properties of OLS estimates for the parameters of SLR when the errors are periodically correlated. In the time series framework it is found that many real time series exhibit periodic autocorrelations that can not be modelled by ordinary seasonal ARMA models (Tiao and Grupe, 1980;Franses and Paap, 2004;McLeod, 1995 …”

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confidence: 99%

On Least Squares Estimation in a Simple Linear Regression Model with Periodically Correlated Errors: A Cautionary Note

Smadi

Abu-Afouna

2016

AJS

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In this research the simple linear regression (SLR) model with autocorrelated errors is considered. Traditionally, correlated errors are assumed to follow the autoregressive model of order one (AR (1)). Beside this model we will also study the SLR model with errors following the periodic autoregressive model of order one (PAR (1)). The later model is useful for modeling periodically autocorrelated errors. In particular, it is expected to be useful when the data are seasonal. We investigate the properties of the least squares estimators of the parameters of the simple regression model when the errors are autocorrelated and for various models. In particular, the relative efficiency of those estimates are obtained and compared for the white noise, AR(1) and PAR(1) models. Also, the generalized least squares estimates for the SLR with PAR(1) errors are derived. The relative efficiency of the intercept and slope estimates based on both methods is investigated via Monte-Carlo simulation. An application on real data set is also provided. It should be emphasized that once there are sufficient evidences that errors are autocorrelated then the type of this autocorrelation should be uncovered. Then estimates of model's parameters should be obtained accordingly, using some method like the generalized least squares but not the ordinary least squares. Zusammenfassung

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“…In order to enable binary-interval-based techniques such as Haar + and CHH to perform smoothly, we have used binary data sizes. Our first data set 1 (FR) is discussed in [33]; it contains a sequence of the mean monthly flows of the Fraser River at Hope, B.C. The flows present periodic autoregression features, while they average at 2709 with standard deviation 2123 and feature discontinuities (min value: 482, max value: 10800).…”

mentioning

confidence: 99%

Optimality and scalability in lattice histogram construction

Karras

2009

Proc. VLDB Endow.

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The Lattice Histogram is a recently proposed data summarization technique that achieves approximation quality preferable to that of an optimal plain histogram. Like other hierarchical synopsis methods, a lattice histogram (LH) aims to approximate data using a hierarchical structure. Still, this structure is not defined a priori; it consists an unknown, not a given, of the problem. Past work has defined the properties that an LH needs to obey and developed general-purpose approximation algorithms for the construction thereof. Still, two major issues remain unaddressed: First, the construction of an optimal LH for a given error metric is a problem unsolved to date. Second, the proposed algorithms suffer from too high space and time complexities that render their application in real-world settings problematic. In this paper, we address both these questions, focusing on the case that the target error metric is a maximum error metric. Our algorithms treat both the error-bounded LH construction problem, in which the space occupied by an LH is minimized under an error constraint, as well as the classic space-bounded problem. First, we develop a dynamicprogramming scheme that detects an optimal LH under a given maximum-error bound. Second, we propose an efficient, practical, greedy algorithm that solves the same problem with much lower time and space requirements. Then, we show how both our algorithms can be applied to the classic space-bounded problem, aiming at minimizing error under a bound on space. Our experimental study with real-world data sets shows the effectiveness of our methods compared to competing summarization techniques. Moreover, our findings show that our greedy heuristic performs almost as well as the optimal solution in terms of accuracy.

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Diagnostic Checking of Periodic Autoregression Models With Application

Cited by 124 publications

References 25 publications

Periodic Seasonal Reg-ARFIMA–GARCH Models for Daily Electricity Spot Prices

Periodic Seasonal Reg-ARFIMA–GARCH Models for Daily Electricity Spot Prices

On Least Squares Estimation in a Simple Linear Regression Model with Periodically Correlated Errors: A Cautionary Note

Optimality and scalability in lattice histogram construction

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