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Topic: Covariance-stationary

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Stationary process - Wikipedia, the free encyclopedia Transforming this data to leave a stationary data set for analysis is referred to as de-trending. In the mathematical sciences, a stationary process (or strict(ly) stationary process) is a stochastic process in which the probability density function of some random variable X does not change over time or position. A discrete-time stationary process where the sample space is also discrete (so that the random variable may take one of N possible values) is known as a Bernoulli scheme. en.wikipedia.org /wiki/Covariance-stationary

* Variance - (Business): Definition covariance stationary: A stochastic process is covariance stationary if neither its mean nor its autocovariances depend on the time or spatial index. The beta is the covariance of the stock in relation to the rest of the stock market. In finance, covariance is applied to the annual rates of return of different investments,... en.mimi.hu /business/variance.html

Classes of Nonseparable, Spatio-temporal Stationary Covariance Functions - Cressie, Huang (ResearchIndex) Abstract: Suppose that a random process Z(s; t), indexed in space and time, has a spatio-temporal stationary covariance C(h; u), where h 2 IR d (d 1) is a spatial lag and u 2 IR is a temporal lag. Cressie, N. & Huang, H. (1999), `Classes of nonseparable spatio-temporal stationary covariance functions', Journal of the American Statistical Association 94(448), 1330-1340. @misc{ cressie99classes, author = "N. Cressie and H. Huang", title = "Classes of nonseparable spatio-temporal stationary covariance functions", text = "Cressie, N. & Huang, H. (1999), `Classes of nonseparable spatio-temporal stationary covariance functions', Journal of the American Statistical Association 94(448), 1330-1340.", year = "1999", url = "citeseer.ist.psu.edu/cressie99classes.html" } citeseer.ist.psu.edu /cressie99classes.html

EconPort - Glossary Any zero mean, covariance stationary process can be represented as a moving average sum of white noise processes plus a linearly deterministic component that is a function of the index t. That any covariance stationary stochastic process with mean zero has a moving average representation, called its Wold decomposition. A random process is weakly stationary iff it is covariance stationary. www.econport.org:8080 /econport/request?page=web_glossary&glossaryLetter=W

Adaptive Covariance Estimation Of Locally Stationary Processes - Mallat, Papanicolaou, Zhang (ResearchIndex) Abstract: We show that the covariance operator of a locally stationary process has approximate eigenvectors that are local cosine functions. @article{ mallat98adaptive, author = "S. Mallat and G. Papicolaou and Z. Zhang", title = "Adaptive covariance estimation of locally stationary processes", journal = "Annals of Statistics", volume = "26", number = "1", pages = "1--47", year = "1998", url = "citeseer.ist.psu.edu/article/mallat95adaptive.html" } Mallat, S., Papanicolaou, G. and Zhang, Z. (1995) Adaptive covariance estimation of locally stationary processes. citeseer.ist.psu.edu /35867.html

Statistical Characteristics A covariance stationary process where the mean of each path realization is random is not ergodic. Such a process is neither strictly stationary nor covariance stationary, but its first-order difference may be. A convenient assumption for the statistical inference based on a time series is that the underlying stochastic process is covariance stationary. mywebpages.comcast.net /ylding/returns/html/node2.html

Aquatic Ecosystem Health and Management Society The commonly employed statistical techniques for estimating both measures presume the data were generated by a covariance stationary process. However, if the assumption of covariance stationarity is violated, the resulting sample variance and variance of the sample mean estimates are biased. In either case, estimates of the sample variance and mean of the sample variance are crucial to making appropriate statistical inferences. www.aehms.org /jaeh_2_3_power.html

Glossary of research economics Covariance stationary means the same as weakly stationary and generally the same as just stationary. Contexts: IO covariance stationary: A stochastic process is covariance stationary if neither its mean nor its autocovariances depend on the time or spatial index. In that equation the process is assumed to be covariance stationary. econterms.com /econtent.html

Book review Stationary ARMA models are introduced via solutions of stochastic difference equations without using the traditional backward shift operator. The last two chapters contain descriptions of stationary sequences in Hilbert spaces and applications of Hardy spaces. The Wold decomposition theorem is proved, and used in computing predictors and the corresponding error variances. www.math.niu.edu /~pourahm/review1.html

GRB - An Investigation of the Unconditional Distribution of South African Stock Index Returns All the futures indexes have excess kurtosis and none of them is covariance stationary. None of these indexes is covariance stationarity over the sample period; this may be due to structural changes in the market such as the introduction of an electronic trading system in 1996 and the volatility introduced by the Asian crisis. For the futures indexes, we find that only the Gold Index is characterized by (positive) skewness. www.globalresearchbusiness.com /paperdis.php?pid=638

bibliog0.html "Estimation of the cross-spectrum of a stationary bivariate stationary on a finite time interval," Biometrika, Vol. stationary point process," Journal of the Royal Statistical Society B www.stat.berkeley.edu /users/brill/bibliog0.html

UAlbany Department of Economics However, the normality assumption is then relaxed, and the results are naturally extended to the case of covariance stationary errors with unknown serial correlation. There are two types of stationary equilibria: one in which all agents conform to the societal norm, and a second involving social stratification on the basis of productivity into two or three groups. The main conclusion is that the tax structure, in that it affects behavior which in turn affects sentiments, plays a crucial role in determining which type of equilibrium occurs and its characteristics as well as the extent of altruism and social cohesion in society. www.albany.edu /econ/Research/Working%20Papers.htm

Abteilung Medizinische Biometrie und Statistik Many statisticians are reluctant to investigate the magnitude of effect within subgroups of the population because of the high probability of spurious results. This application involves a seasonal effect, a potentially non-linear covariate effect, a repeated measurements error structure and the comparison of different groups of data. Regulatory bodies, while often stating their discomfort with subgroup and covariate analysis, sometimes craft labeling statements about new drugs in terms of inference from subgroups. www.ibc2002.uni-freiburg.de /ScientificProgram/InvitedPaperSessionall.html

Citations: The econometrics of financial markets - Adrian (ResearchIndex) Moreover an integrated EGARCH process is neither strictly stationary nor covariance stationary. Our basic idealisation is that returns follow a stationary time series model with stochastic volatility structure. or stretched exponentials [14] as well as models allowing for non stationary of volatility such as ARCH and GARCH models [15] which better reproduces the statistics of the market uctuations. citeseer.ist.psu.edu /context/293793/0

Current Issues The computations of the relevant Wald test statistic presupposes that variables entering the vector autoregression (VAR) specification are covariance stationary. The stationary linear combination is called the cointegrating equation and mav be interpreted as a long-run equilibrium relationship between the variables. Engle and Granger (1987) point out that a linear combination of two or more non-smionary series may be stationary, or I(O), and the non-stationary time series are said to be cointegrated. www.journalofpolicymodels.com /stephen.shtml

Testing for Unit Roots is not stationary, although we know it to be stationary both before and after the break at t=50. That is, the mean, variance and covariance are invariant to the time origin. Phillips and Perron have devised corrected test statistics for the instances in which the error is an MA, is perhaps heterogeneous, or there is a structural break in the data. isc.temple.edu /economics/notes/unitroot/Test1root.HTM

richard.html We investigate then the alternative use of the Garch(1,1) process as a local, stationary approximation of the data and find that the Garch(1,1) model fails during significantly long periods to provide a good local description to the time series of returns on the S&P 500 and Dow Jones Industrial Average indexes. We investigate the relevance of the stationary, non-linear, conditional, parametric modeling paradigm embodied by the Garch(1,1) process to describing and forecasting the dynamics of returns of the Standard & Poors 500 (S&P 500) stock market index. We develop a non-parametric, non-stationary framework for business-cycle dating based on an innovative statistical methodology known as Adaptive Weights Smoothing (AWS). www.math.ku.dk /~mikosch/maphysto_richard/richard.html

New Page 1 If it can be demonstrated that a particular net discount rate is covariance stationary (i.e., exhibits random fluctuations around a constant long-term mean), it can be argued that such an historical NDR may be appropriate for present value calculations. Conversely, if a particular NDR is nonstationary, the historical long-run NDR probably has little predictive power. Specifically, the time-series properties of various medical care net discount rates are analyzed. www.journaloflegaleconomics.com /abstracts/ABbow.htm

covariance - OneLook Dictionary Search Phrases that include covariance: covariance matrix, analysis of covariance, serial covariance, covariance assets, covariance stationary, more... Covariance : AMEX Dictionary of Financial Risk Management [home, info] Tip: Click on the first link on a line below to go directly to a page where "covariance" is defined. www.onelook.com /?loc=rescb&w=covariance

4. PUBLICATIONS AND EDITING ACTIVITIES The class of locally stationary wavelt is a wavelet-based model for covariance nonstationary zeromean time series. DONOHO, D.L., MALLAT, S., von SACHS, R. and Y. Locally stationary covariance and signal estimation with macrotiles. A notion of time­varying wavelet spectrum is uniquely defined as a wavelet­type transform of the autocovariance function with respect to so­called autocorrelation wavelets. www.stat.ucl.ac.be /ISrapport/rapeng03/node5.html

lec_etrx_7.doc The strong form is generally regarded as being too strict so we will concern ourselves with weak stationarity, sometimes known as covariance stationary, wide-sense stationary or second-order stationary. A univariate time series, yt, is said to be stationary if its mean, variances, and auto-covariances are independent of time. The conditions require the mean, variance, and autocovariances to be independent of time. www.sussex.ac.uk /economics/documents/lec_etrx_7.doc

Modeling and Simulation Since a Gaussian process needs a mean and covariance matrix only, it is stationary (strictly) if it is covariance stationary. A stochastic process is a second order stationary if it is first order stationary and covariance between X(t) and X(s) is function of t-s only. In simulation output statistical analysis we are satisfied if the output is covariance stationary. home.ubalt.edu /ntsbarsh/simulation/sim.htm

2004fe19 the immediate price impacts of market orders) are well described by covariance stationary processes. The in-sample, 1-step ahead point predictions for these curves perform well and motivate the development of parametric FSN models that take into account the monotonicity of the price curves and can be used to form predictive distributions. It is found that the differences between the bid and ask curves and their intercepts (i.e. www.finance.ox.ac.uk /pages_fineconpapers/2004fe19.htm

Undergraduate Multivariate normal samples: Estimation of the mean vector and covariance matrix, estimation of correlation coefficients, distribution of the sample mean, sample covariance matrix and sample correlation coefficients. The linear model: modes of full rank, least squares estimators, test of hypotheses. www.up.ac.za /academic/stats/undergraduate.htm

Recent Research It is shown that the approximate slopes of regression tests are at least as great as those based on the residuals of univariate ARIMA models, and that there are cases in which the former are arbitrarily great while the latter are arbitrarily small. To provide an empirical example a latent variable model for permanent income is developed, its parameters are shown to be identified, and a variety of restrictions on these parameters implied by the permanent income hypothesis are tested. By mixing on both the mean and variance parameters and by increasing the number of distributions in the mixture these models effectively remove the normality assumption and are much closer to semiparametric models. www.biz.uiowa.edu /faculty/jgeweke/papers.html

Working Paper 99-06 Price series that are 21.5 years long for six agricultural futures markets, corn, soybeans, wheat, hogs, coffee, and sugar, exhibit time-varying volatility, carry long-range dependence, and portray excessive skewness and kurtosis, though they are covariance stationary. www.ace.uiuc.edu /ofor/wp0400ab.htm

Cornell Econ Dept - Faculty - Yongmiao Hong Time series and generalized spectral analysis; serial independence tests; diagnostic checking of time series models; wavelet analysis; heteroskedasticity and auto correlation consistent covariance matrix estimation; inference and forecast of exchange rates; nonparametric specification testing for continuous-time diffusion models; evaluation of out-of-sample probability density forecasts and value-at-risk forecasts; China's economic reforms. www.arts.cornell.edu /econ/faculty/hong.html

EconPapers: Modeling Sequences of Long Memory Positive Weakly Stationary Random Variables Unlike FIGARCH model of Baillie, Bollerslev and Mikkelsen (1996), our models are weakly stationary with non-summable autocovariances and hence belong to the class of long-memory models according to the criteria of McLeod and Hipel (1978). Abstract: In this paper we introduce a new class of covariance stationary long-memory models on the positive half-line. Modeling Sequences of Long Memory Positive Weakly Stationary Random Variables econpapers.repec.org /paper/wdipapers/2002-493.htm

Citations: Forecasting Economic Time Series - Granger, Newbold (ResearchIndex) 310) therefore propose a natural measure of the forecastability of covariance stationary series under squared error loss, patterned after the familiar R 2 of linear regression, where is the optimal (i.e. It may be tempting to simply compare the expected losses of forecasts for two series to assess their relative predictability, but that ignores the possibility that the two series may be measured on different scales. citeseer.ist.psu.edu /context/41204/0

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