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Finance Menu

Activate the finance menu. The following options and facilities are available:

Price Return Transformation
GARCH(p,q) process
Moving Estimates (Sample, Gaussian, GP)


Price Return Transformation

It is assumed that there is a data set of type Xtremes Multivariate Data with the date (format: day-month-year) in the first three columns and speculative prices in the fourth (and further) columns. If necessary, apply the Select Columns option. If dates are included which are not trading days then indicate the missing price by a period.

A single speculative asset:

Apply Price Return Transformation to transform prices into log-returns r[t] = log(p[t]) - log(p[t-1]) of prices for consecutive trading days. Gaps between trading days (the weekend effect) are dealt with in the following manner:
  1. Trading days, log-returns: the dates of the trading days and the pertaining log-returns are stored in a file.
  2. All days, log-returns, missing values: compared to (a), the "weekend" dates are included and the missing log-returns are indicated by -1.
  3. Omit "Monday" log-returns: compared to (a), the days after a gap are omitted. Thus, e.g., after a weekend the Monday returns are omitted.
  4. Distribute "Monday" log-returns: the return registered after a gap (e.g., the return recorded on Monday) is equally distributed over the relevant days (e.g., if r is the return on Monday, then r/3 is taken as the return on Saturday, Sunday and Monday).
The resulting data set has the number of the day in the first column, the date in the next three columns and the log-returns (respectively, the missing return is indicated by -1) in the fifth column.

Several speculative assets:

This operation can also be simultaneously applied to several speculative prices.

GARCH(p,q) process

This facility allows the simulation of GARCH(p,q) series for p >= 0 and q >= 1. Recollect that an ARCH(p) series is a GARCH(p,0) series. The following parameters must be specified in edit fields.
Coefficients
Enter non-negative coefficients alpha[i], i = 0,..., p, and beta[j], j=1,...,q, separated by blanks, as required by the GARCH(p,q) equation (see Statistical Analysis, equation (13.42)). If q = 0, then enter no value for beta or a zero to get an ARCH series.
Initializing time
Enter an initializing time span, i.e the number of values that are computed in advance to stabilize the time series. The GARCH(p,q) series consists of those values generated afterwards.
Qf of innovations
Enter a quantile function of the innovations epsilon[t]. Use the predefined function calls provided by the User Formula facility. For example, enter gaussianqf(x) or paretoqf(2,x) in the edit field to include standard Gaussian or standard Pareto (under the shape parameter alpha = 2) innovations.
Additional remarks
Sample Size positive integer
Filename Select a filename, and, optionally, a directory.

The stored data set is now the active one.

Moving Estimates (Sample, Gaussian, GP)

The subsequent procedures are applicable to data (t[i],y[i]) of type Xtremes Time Series. The primary intention is to create a platform for analyzing "time-varying" parameters for financial data. It would be interesting to see applications in other fields.

The "sample mean" procedure is nearly identical to the Moving Average procedure in the local menu of the scatterplot window, yet one should keep in mind that

the output is given in a plot window instead of a scatterplot window,
the "average", if evaluated at t[k] is taken w.r.t.
y[k-m], ... , y[k] (left-sided)
y[k-m], ... , y[k+m] (two-sided)
with "left-sided" as a default option.

Here comes an overview of the available procedures (a sample version and estimation within the Gaussian and GP models).
Moving Estimates (Sample) Mean Standard Deviation
Variance VaR
Moving Estimates (Gaussian) Mean Standard Deviation
Variance VaR
Moving Estimates (GP) Scale Parameter Shape Parameter Gamma
VaR

Moving Estimates (Sample)

Moving Estimates (Sample Mean)
The sample mean for the chosen time horizon is plotted against time with "left-sided" as the default option.

Moving Estimates (Sample Standard Deviation)
The sample standard deviation for the chosen time horizon is plotted against time with "left-sided" as the default option.

Moving Estimates (Sample Variance)
The sample variance for the chosen time horizon is plotted against time with "left-sided" as the default option.

Moving Estimates (Sample VaR)
The sample VaR at the level q for the chosen time horizon is plotted against the time with "left-sided" as the default option. Thus, one is evaluating the sample q-quantile.

Moving Estimates (Gaussian)

The MLEs within the Gaussian model are employed to estimate the same parameters as those in the empirical approach. Therefore, the estimates of the mean, standard deviation and variance are closely related to those in the empirical case.

Moving Estimates (Gaussian Mean)
The sample mean (MLE in the Gaussian model) for the chosen time horizon is plotted against time with "left-sided" as the default option.

Moving Estimates (Gaussian Standard Deviation)
The MLE for the scale parameter in the Gaussian model evaluated for the chosen time horizon is plotted against time with "left-sided" as the default option.

Moving Estimates (Gaussian Variance)
The MLE for the variance in the Gaussian model evaluated for the chosen time horizon is plotted against time with "left-sided" as the default option.

Moving Estimates (Gaussian VaR)
The MLE for the mean and variance in the Gaussian model is evaluated for the chosen time horizon. The q-quantile of estimated Gaussian distribution is plotted against time. This approach enables an extrapolation beyond the range of the data.

Moving Estimates (GP)

The primary aim is to estimate the VaR over a moving window (for the chosen time horizon) using the POT method. Estimates of the scale and shape parameters are added.
Besides the time horizon choose the number of upper order statistics. Select one of the estimators in GP models. The estimation is carried out in the gamma-parametrization.

Moving Estimates (GP Scale Parameter)
The estimate of the scale parameter within the model of truncated GP distribution evaluated for the chosen time horizon is plotted against time with "left-sided" as the default option.

Moving Estimates (GP Shape Parameter Gamma)
The estimate of the shape parameter within the model of (truncated) GP distribution evaluated for the chosen time horizon is plotted against time with "left-sided" as the default option.

Moving Estimates (GP VaR)
Estimates of the scale and shape parameters in the model of truncated GP distributions are evaluated w.r.t. the chosen time horizon. This GP distribution is transformed in the usual manner so that the transformed GP distributions represents the original data in the upper tail. The q-quantile of the transformed distribution is plotted against time. This approach enables an extrapolation beyond the range of the data.

© 2005
Xtremes Group · updated Jun 21, 2005