Covers important modern topics such as time series forecasting, volatility modeling, switching models and simulation methods. Cambridge University Press has no responsibility for the continuity or accuracy of URLs to external or third-party Internet sites referred to in this publication and does not warrant that any content on such sites is or will remain accurate or appropriate.
A review of some fundamental mathematical and
Value of GEYR and probability of it being in the High GEYR regime for the.
Screenshots
Preface to the second edition
What is econometrics?
The first four letters of the word correctly suggest that the origins of econometrics are rooted in economics. The list in Box 1.1 is, of course, by no means exhaustive, but hopefully gives some flavor of the usefulness of econometric tools in terms of their financial applicability.
Is financial econometrics different from ‘economic econometrics’?
Similarly, some sets of financial data are observed at much higher frequencies than macroeconomic data. Moreover, the analysis of financial data brings with it a number of new problems.
Types of data
Note that, unlike the time series example, there is no natural order of observations in a cross-sectional sample. On the other hand, in the context of a time series, the order of the data is important, as the data is usually arranged chronologically.
Returns in financial modelling
The academic finance literature usually uses the log-return formulation (also known as log-price related, as it is the log of the ratio of this period's price to the previous period's price). In the limit, as the frequency of sampling the data is increased so that they are measured over a smaller and smaller time interval, the simple and continuously compounded returns will be identical.
Steps involved in formulating an econometric model
Alternatively, the required data may only be available via a survey after sending out a set of questionnaires, i.e. primary data. Often the final preferred model may be very different from the one originally proposed and need not be unique in the sense that another researcher with the same data and the same initial theory could arrive at a different final specification.
Points to consider when reading articles in empirical finance As stated above, one of the defining features of this book relative to others
Is the sample size sufficiently large for the model estimation task at hand? Have tests been conducted for possible violations of any assumptions made in estimating the model?
Econometric packages for modelling financial data
Descriptive summary statistics for a series can be obtained by selecting Quick/Series Statistics/Histogram and Statistics and entering the name of the variable (DHP). From the main menu, select Quick/Graphhand enter the name of the series you want to plot (HP to plot the level of house prices) and click OK.
Outline of the remainder of this book
Chapter 40, the last chapter of the manual, explains how to perform factor analysis in EViews. Examples of the huge number of applications are discussed, with particular reference to stock returns.
Further reading
Readers will learn how to construct, estimate, and interpret such models, and how to distinguish and select alternative specifications. Some tentative suggestions are also provided for potential areas of growth in financial time series modeling.
What is a regression model?
There are various completely interchangeable names for y and xs, and all of these terms will be used synonymously throughout this book (see Box 2.1).
Regression versus correlation
Simple regression
This can be seen as equivalent to minimizing the sum of the areas of the squares drawn from the points to the line. Again, the first step could be to form a scatterplot of the two variables (Figure 2.5).
Some further terminology
In such cases, one could not expect to obtain robust estimates of the value of y when x is zero, since all the information in the sample relates to the case where x is significantly greater than zero. Similarly, if theory suggests that x must be inversely related to y according to a model of the form
Simple linear regression in EViews – estimation of an optimal hedge ratio
Now estimate a regression for the levels of the series rather than the returns (i.e. run a regression of dot on a constant and future) and examine the parameter estimates. This issue of the long and short runs will be discussed in detail in chapter 4.
In contrast, the slope parameter in a regression using the raw spot and futures indices (or the log of the spot series and the log of the futures series) can be interpreted as measuring the long-run relationship between them. The intercept can be considered an approximation of the carry costs, while as expected the long-term relationship between spot and futures prices is almost 1:1 – see Chapter 7 for further discussion of the estimation and interpretation of this long-term relationship. term relationship.
Properties of the OLS estimator
In the limit (i.e., for an infinite number of observations), the probability that the estimator differs from the true value is zero. The assumptions that E(xtut)=0 and E(ut)=0 are sufficient to derive the consistency of the OLS estimator.
Precision and standard errors
It is possible, of course, to derive formulas for the standard errors of the coefficient estimates from first principles using some algebra, and Now, returning to standard error calculations, it is necessary to obtain an estimate of the error variance.
An introduction to statistical inference
If the null hypothesis is rejected at the 5% level, the result of the test is said to be 'statistically significant'. If the null hypothesis is not rejected, the result of the test would be said to be 'not significant', or it would be said to be 'insignificant'.
A special type of hypothesis test: the t -ratio
The power of the test is also equal to one minus the probability of a type II error. The ratios associated with each intercept and slope coefficient would be given by .
An example of the use of a simple t -test to test a theory in finance: can US mutual funds beat the market?
As table 2.4 shows, the average (defined as either the mean or the median) fund failed to 'beat the market', recording a negative alpha in both cases. Given that a nominal 5% two-sided test size is used, one would expect two or three funds to 'significantly beat' the market by chance.
Can UK unit trust managers beat the market?
This variability is further demonstrated in figure 2.19, which plots the value of £100 invested in each of the funds in January 1979 over time. Second, gross of transaction costs, nine funds from the sample of 76 were able to significantly outperform the market by providing a significant positive alpha, while seven funds produced significant negative alphas.
The overreaction hypothesis and the UK stock market
The first regression to be performed is the excess return of losers over winners on only one constant. In the second regression test, βˆ represents the difference between the market betas of the winning and losing portfolios.
The exact significance level
Remember that the estimated value of the coefficient in a regression of a variable on only one constant is equal to the average value of this variable. The p-value has also been termed the 'plausibility' of the null hypothesis; so the smaller the p-value, the less plausible the null hypothesis.
Hypothesis testing in EViews – example 1: hedging revisited
Informally, the p-value is also often called the probability of error when the null hypothesis is rejected. In this case, you should find that the null hypothesis is not rejected (table below).
Estimation and hypothesis testing in EViews – example 2
How could the hypothesis that the value of the population coefficient is equal to 1 be tested. 2A.2 Derivation of the OLS standard error estimators for the intercept and slope in the bivariate case.
Generalising the simple model to multiple linear regression
But it is more important and valid to have more than one explanatory variable in the regression equation at the same time, and therefore to examine the effect of all the explanatory variables together on the explained variable. Each coefficient is now known as a partial regression coefficient, interpreted as representing the partial effect of the given explanatory variable on the explained variable, after holding all other explanatory variables constant or having their effect eliminated.
The constant term
Thus, there is implicitly a variable hidden next to β1, which is a column vector of ones, whose length is the number of observations in the sample. This corresponds to the number of parameters estimated in the regression equation.
How are the parameters (the elements of the β vector) calculated in the generalised case?
The denominator of (3.9) is given by T−2, which is the number of degrees of freedom for the bivariate regression model (that is, the number of observations minus two). Informally, the number of constraints can be thought of as 'the number of equality signs under the null hypothesis'.
Sample EViews output for multiple hypothesis tests
Multiple regression in EViews using an APT-style model
Remember that this tests the null hypothesis that all the slope parameters are jointly zero. In the second box, 'List of search regressors', type the list of all the explanatory variables used above: ERSANDP DPROD DCREDIT DINFLATION DMONEY DSPREAD RTERM.
Data mining and the true size of the test
An approximation to the asymptotic behavior of the test statistic can be obtained using finite samples, provided they are large enough. Testing many variables in a regression without basing the choice of candidate variables on a financial or economic theory is known as
Goodness of fit statistics
The total variation across all observations of the dependent variable about its mean is. In the second case, the model explained all the variability in ya about its mean value, which means that the residual sum of squares will be zero.
Hedonic pricing models
The actual signs of the coefficients can be compared with their expected values, given in the last column of table 3.1 (as determined by this author). The coefficient estimates themselves show the Canadian dollar rental price per month of each characteristic of the dwelling.
Tests of non-nested hypotheses
Therefore, a test for the best model will be performed by an examination of the significances of γ2 and γ3 in model (3.50). In this case, none of the models can be abandoned, and another method of choosing between them must be used.
Mathematical derivations of CLRM results
This quantity, s2(XX)−1, is known as the estimated variance-covariance matrix of the coefficients. The variance of βˆ1 is the first diagonal element, the variance of βˆ2 is the second element on the leading diagonal,.
A brief introduction to factor models and principal components analysis
- Introduction
- Statistical distributions for diagnostic tests
- Assumption 1: E(u t ) = 0
- Assumption 2: var(u t ) = σ 2 < ∞
- Assumption 5: the disturbances are normally distributed
- Multicollinearity
- Adopting the wrong functional form
The denominator of the test statistic is simply (number of observations . −1)×variance of residuals. In this case, it is not possible to estimate all coefficients in the model.
