The Garch-in-mean (MGARCH) model adds the equation’s variance to the regression function. This allows the average value of the dependent variable to depend on volatility of the underlying asset. In this way, more risk (volatility) can lead to higher average return. The equations are listed below:
yt = во + Oht + et (14.9)
ht = 5 + aief-1 + ydt-ie-! + eiht-i (14.10)
Notice that in this formulation we left the threshold term in the model. The errors are normally distributed with zero mean and variance ht.
The parameters of this model can be estimated using gretl, though the recursive nature of the likelihood function makes it a bit more difficult. In the script below (Figure 14.9) you will notice that we’ve defined a function to compute the log-likelihood.2 The function is called g... Read More
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B... Read More
The following script estimates the reduced form equations using least squares and the demand equation using two-stage least squares for Graddy’s Fulton Fish example.
In the example, ln(quan) and ln(price) are endogenously determined. There are several potential instruments that are available. The variable stormy may be useful in identifying the demand equation. In order for the demand equation to be identified, there must be at least one variable available that effectively influences the supply of fish without affecting its demand. Presumably, stormy weather affects the fishermen’s catch without affecting people’s appetite for fish! Logically, stormy may be a good instrument.
The model of demand includes a set of indicator variables for day of the week... Read More
Obtaining confidence intervals for the marginal effects (and the AME) is relatively straightforward as well. To estimate the standard error of the marginal effect, we resort to the Delta method. This method of finding the variance of functions of parameters was discussed in section 5.3.2. You may want to take a look at this section again (page 99), before proceeding.
Using the Delta method means taking analytic or numerical derivatives of the marginal effect or AME to be used in the computation of the standard error of the AME. The analytic derivatives are not that hard to take, but why bother when numerical ones are available. This is the approach taken in commercial software that includes the ability to estimate nonlinear combinations of parameters and their standard errors.
The functi... Read More
Our initial impressions of the data are gained from looking at plots of the two series. The data plots are obtained in the usual way after importing the dataset. The data on U. S. and Australian GDP are found in the gdp. gdt file and were collected from 1970:1 – 2004:4. Open the data and set the data structure to quarterly time-series using the setobs 4 command, start the series at 1970:1, and use the —time-series option.
open "@gretldirdatapoegdp. gdt" setobs 4 1970:1 —time-series
One purpose of the plots is to help you determine whether the Dickey-Fuller regressions should contain constants, trends or squared trends. The simplest way to do this is from the console using the scatters command.
scatters usa diff(usa) aus diff(aus)
The scatters command produces multiple graphs, each ... Read More
The hip data are used to illustrate computations for some simple statistics in your text.
C.1 Summary Statistics
Using a script or operating from the console, open the hip data, hip. gdt, and issue the summary command. This yields the results shown in Table C.1. This gives you the mean, median, miniSummary Statistics, using the observations 1-50 for the variable ‘y’ (50 valid observations)
Standard deviation C. V.
Skewness Ex. kurtosis
Table C.1: Summary statistics from the hip data
mum, maximum, standard deviation, coefficient of variation, skewness and excess kurtosis of your variable(s). Once the data are loaded, you can use gretl’s language to generate these as well. For instance, scalar y_bar = mean(y) yields the mean of the variable y... Read More