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| R2012a Documentation → Econometrics Toolbox | |
Learn more about Econometrics Toolbox |
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| Contents | Index |
A model-order selection criterion based on parsimony. More complicated models are penalized for the inclusion of additional parameters. See also Bayesian information criteria (BIC).
A variance reduction technique that pairs a sequence of independent normal random numbers with a second sequence obtained by negating the random numbers of the first. The first sequence simulates increments of one path of Brownian motion, and the second sequence simulates increments of its reflected, or antithetic, path. These two paths form an antithetic pair independent of any other pair.
Autoregressive. AR models include past observations of the dependent variable in the forecast of future observations.
Autoregressive Conditional Heteroscedasticity. A time series technique that uses past observations of the variance to forecast future variances. See also GARCH.
Autoregressive Moving Average. A time series model that includes both AR and MA components. See also AR and MA.
Correlation sequence of a random time series with itself. See also cross-correlation function (XCF).
See AR.
A model-order selection criterion based on parsimony. More complicated models are penalized for the inclusion of additional parameters. Since BIC imposes a greater penalty for additional parameters than AIC, BIC always provides a model with a number of parameters no greater than that chosen by AIC. See also Akaike information criteria (AIC).
A zero-mean continuous-time stochastic process with independent increments (also known as a Wiener process).
Time series technique with explicit dependence on the past sequence of observations.
time series model for forecasting the expected value of the return series itself.
Time series model for forecasting the expected value of the variance of the return series.
Correlation sequence between two random time series. See also autocorrelation function (ACF).
The function that characterizes the random (stochastic) portion of a stochastic differential equation. See also stochastic differential equation.
Errors that may arise due to discrete-time sampling of continuous stochastic processes.
The function that characterizes the deterministic portion of a stochastic differential equation. See also stochastic differential equation.
A constraint, imposed during parameter estimation, by which a parameter is held fixed at a user-specified value.
A simulation technique that provides a discrete-time approximation of a continuous-time stochastic process.
A characteristic, relative to a standard normal probability distribution, in which an area under the probability density function is reallocated from the center of the distribution to the tails (fat tails). Samples obtained from distributions with excess kurtosis have a higher probability of containing outliers than samples drawn from a normal (Gaussian) density. Time series that exhibit a fat tail distribution are often referred to as leptokurtic.
Time series used to explain the behavior of another observed series of interest. Explanatory variables are typically incorporated into a regression framework.
See excess kurtosis.
Generalized autoregressive conditional heteroscedasticity. A time series technique that uses past observations of the variance and variance forecast to forecast future variances. See also ARCH.
Time-varying, or time-dependent, variance.
Time-independent variance. The Econometrics Toolbox software also refers to homoscedasticity as constant conditional variance.
Independent, identically distributed.
A sequence of unanticipated shocks, or disturbances. The Econometrics Toolbox software uses innovations and residuals interchangeably.
See excess kurtosis.
Moving average. MA models include past observations of the innovations noise process in the forecast of future observations of the dependent variable of interest.
Minimum mean square error. A technique designed to minimize the variance of the estimation or forecast error. See also RMSE.
See MA.
The function to numerically optimize. In the Econometrics Toolbox software, the objective function is the loglikelihood function of a random process.
Correlation sequence estimated by fitting successive order autoregressive models to a random time series by least squares. The PACF is useful for identifying the order of an autoregressive model.
A random trial of a time series process.
A stratified sampling technique that ensures that the proportion of random draws matches its theoretical probability. One of the most common examples of proportional sampling involves stratifying the terminal value of a price process in which each sample path is associated with a single stratified terminal value such that the number of paths equals the number of strata.
See also stratified sampling.
The lowest level of significance at which a test statistic is significant.
See path.
See innovations.
Root mean square error. The square root of the mean square error. See also MMSE.
The innovations divided by the corresponding conditional standard deviation.
A generalization of an ordinary differential equation, with the addition of a noise process, that yields random variables as solutions.
See stratified sampling.
A variance reduction technique that constrains a proportion of sample paths to specific subsets (or strata) of the sample space.
Discrete-time sequence of observations of a random process. The type of time series of interest in the Econometrics Toolbox software is typically a series of returns, or relative changes of some underlying price series.
A response, or behavior, of a time series that is heavily dependent on the initial conditions chosen to begin a recursive calculation. The transient response is typically undesirable, and initially masks the true steady-state behavior of the process of interest.
The result of an independent random experiment that computes the average or expected value of a variable of interest and its associated confidence interval.
Time series technique in which explicit dependence on the past sequence of observations is ignored. Equivalently, the time stamp associated with any observation is ignored.
A sampling technique in which a given sequence of random variables is replaced with another of the same expected value but smaller variance. Variance reduction techniques increase the efficiency of Monte Carlo simulation.
The risk, or uncertainty, measure associated with a financial time series. The Econometrics Toolbox software associates volatility with standard deviation.
See Brownian motion.
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