Normality tests
Let us now consider the fundamental problem of testing disturbance normality in the context of the linear regression model: Y = Xp + u, (23.12) where Y = (y1, ..., …
Univariate Forecasts
Univariate forecasts are made solely using past observations on the series being forecast. Even if economic theory suggests additional variables that should be useful in forecasting a particular variable, univariate …
Further Research on Cointegration
Although the discussion in the previous sections has been confined to the possibility of cointegration arising from linear combinations of I(1) variables, the literature is currently proceeding in several interesting …
Monte Carlo tests based on pivotal statistics
In the following, we briefly outline the MC test methodology as it applies to the pivotal statistic context and a right-tailed test; for a more detailed discussion, see Dufour (1995) …
Duration dependence
The duration dependence describes the relationship between the exit rate and the time already spent in the state. Technically it is determined by the hazard function, which may be a …
Extensions
There are many ways of extending the previous model. For instance, we could allow for different distributions for zi (see Koop et al., 1995) or for many outputs to exist …
AR(1): the probabilistic reduction perspective
The probabilistic reduction perspective has been developed in Spanos (1986). This perspective begins with the observable process {yt, t Є T} and specifies the statistical model exclusively in terms of …
The Hylleberg-Engle-Granger-Yoo test
It is well known that the seasonal difference operator As = 1 - Ls can always be factorized as 1 - Ls = (1 - L)(1 + L + L2 …
The SVD model
This model represents dynamics of both the conditional mean and variance in duration data. In this way it allows for the presence of both conditional under - and overdispersion in …
Definitions and tests
Let X and Y be two income variables at either two different points in time, before and after taxes, or for different regions or countries. Let X1, X2,..., Xn be …
The Gaussian AR(1) Case with Intercept under the Alternative of Stationary
If under the stationarity hypothesis the AR(1) process has an intercept, but not under the unit root hypothesis, the AR(1) model that covers both the null and the alternative is: …
Granger-causality analysis
The concept The causality concept introduced by Granger (1969) is perhaps the most widely discussed form of causality in the econometrics literature. Granger defines a variable y1t to be causal …
Uniform linear hypothesis in multivariate regression models
Multivariate linear regression (MLR) models involve a set of p regression equations with cross-correlated errors. When regressors may differ across equations, the model is known as the seemingly unrelated regression …
Differencing the data
A question that arises in practice is whether to difference the data prior to construction of a forecasting model. This arises in all the models discussed above, but for simplicity …
Higher order cointegrated systems
The statistical theory of I(d) systems with d = 2, 3,..., is much less developed than the theory for the I(1) model, partly because it is uncommon to find time …
Parametric and. Nonparametric Tests. of Limited Domain and. Ordered Hypotheses. in Economics
Esfandiar Maasoumi* 1 Introduction In this survey, technical and conceptual advances in testing multivariate linear and nonlinear inequality hypotheses in econometrics are summarized. This is discussed for economic applications in …
Basic duration distributions
In this section we introduce some parametric families of duration distributions. Exponential family The exponentially distributed durations feature no duration dependence. In consequence of the time-independent durations, the hazard function …
Nonlinear production frontiers
The previous models both assumed that the production frontier was log-linear. However, many common production functions are inherently nonlinear in the parameters (e. g. the constant elasticity of substitution or …
Extending the autoregressive AR(1) model
The probabilistic reduction (PR) perspective, as it relates to respecification, provides a systematic way to extend AR(1) in several directions. It must be emphasized, however, the these extensions constitute alternative …
Extensions to the HEGY approach
Ghysels, Lee, and Noh (1994), or GLN, consider further the asymptotic distribution of the HEGY test statistics for quarterly data and present some extensions. In particular, they propose the joint …
Simulation Based. Inference for. Dynamic Multinomial. Choice Models
John Geweke, Daniel Houser,and Michael Keane multinomial choice histories and partially observed payoffs. Many general surveys of simulation methods are now available (see Geweke, 1996; Monfort, Van Dijk, and Brown, …
1 Introduction, History, and Definitions
If Xt, Yt are a pair of time series, independent of each other and one runs the simple ordinary least squares regression Yt = a + bXt + e t, …
General AR Processes with a Unit Root, and the Augmented Dickey-Fuller Test
The assumption made in Sections 2 and 3 that the data-generating process is an AR(1) process, is not very realistic for macroeconomic time series, because even after differencing most of …
Impulse response analysis
Tracing out the effects of shocks in the variables of a given system may also be regarded as a type of causality analysis. If the process yt is I(0), it …
Nonparametric. Kernel Methods. of Estimation and. Hypothesis Testing
Aman Ullah* 1 Introduction Over the last five decades much research in empirical and theoretical econometrics has been centered around the estimation and testing of various econometric functions. For example …
Econometric applications: discussion
In many empirical problems, it is quite possible that the exact null distribution of the relevant test statistic S(Y) will not be easy to compute analytically, even though it is …
Empirical examples
We now turn to applications of some of these forecasting methods to the five US macroeconomic time series in Figures 27.1-27.5.2 In the previous notation, the series to be forecast, …
Fractionally cointegrated systems
As discussed earlier in this chapter, one of the main characteristics of the existence of unit roots in the Wold representation of a time series is that they have "long …
Nonlinear models
Outside of the normal distribution, conditional expectations are typically nonlinear, and in general one would imagine that these infeasible optimal forecasts would be nonlinear functions of past data. The main …
Parametric Models
In empirical research we may wish to investigate the dependence of individual hazard functions on exogenous variables. These variables, called the control variates, depict in general various individual characteristics. Let …
The Stochastic Frontier Model with Panel Data
3.1 Time-invariant efficiency It is increasingly common to use panel data13 in the classical econometric analysis of the stochastic frontier model. Some of the statistical problems (e. g. inconsistency of …
Moving Average Models
3.2 The traditional approach A moving average model of order q, denoted by MA(q): q yt = a0 + X akzt-k + £t, ^ ~ NI(0, a2), t Є T, …
Multiple tests and levels of significance
It is notable that many tests of the seasonal unit root null hypothesis involve tests on multiple coefficients. In particular, for the application of the HEGY test (31.44), Hylleberg et …
The Dynamic Multinomial Choice Model
In this section we present an example of Bayesian inference for dynamic discrete choice models using the Geweke-Keane method of replacing the future component of the value function with a …
Simulations
The obvious way to find evidence of spurious regressions is by using simulations. The first simulation on the topic was by Granger and Newbold (1974) who generated pairs of independent …
