Regression Analysis: Tesco Plc, Taylor Wimpey vs. FTSE 100 (Statistics Project Sample)

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4. For each stock, regress the stock return against the market return. Explain your results.
Regression Analysis Tesco Plc. vs. FTSE 100
We start by performing a t-test to make a conclusion about the slope parameter,β.
T-test:
t= (estimate-hypyezised value)stander error
To conclude that β is not one and, therefore, no causality, the absolute t value must be larger than the critical value.
t= (1.1877-1)0.1596= 1.176
From this, we could conclude that t is not significantly different from one.
The standard error is slight, and the R-squared is very low 0.26.
There is no heteroscedasticity, and the model is not normally distributed.
Regression Analysis Taylor Wimpey vs. FTSE 100
T-test:
t= (estimate-hypyezised value)stander error
To conclude that β is not 1 and, therefore, no causality, the absolute t value must be larger than the critical value.
t= (1.4693-1)0.1576= 2.9778
From this, we could conclude that t is significantly different from 1.
The standard error is minuscule, and the R-squared is very low 0.36.
There is no heteroscedasticity, and the model is usually distributed (Anderson, 2000,120
1 Test for the presence of unit roots in the three series. Explain carefully the testing procedure used.
A time series model is said to be stationary if its joint distribution is time invariant and, therefore, not all the cross-sectional moments of the distribution, that is the mean and may be variance depend on time and most importantly that covariance remains constant across time.
Many economic variables including GDP, Labor force, and money supply are non-stationary, and Dickey-Fuller and Augmented Dickey-Fuller test can be used to check for this with the null hypothesis of existence of a unit root
To check and test for unit root we use the Augmented Dickey-Fuller (ADF) unit root test. The ADF regression equations are:
Yt= ßYt-1+ε t
The null hypothesis attempts to check whether the variables are stationary or not as shown below;
H0: ß= 1 Unit root/Non-stationary
HA: ß< 1 Stationary
in case null hypothesis is valid it implies that the data is non-stationary data, hence null hypothesis is rejected, the data has no unit root and hence stationary.
Unit Root Test Tesco
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From the above test at both lag 6 and five respectively the p-values are less than 0.05, reject the null hypothesis meaning Tesco return series is stationary. Stationary, which also implies the absence of a unit root, is inferred to imply that the return series on the above data converges to a constant.
Unit Root Test Taylor Wimpey
From the above test at both lag 3 and two respectively the p-values are less than 0.05, hence reject the null hypothesis and conclude that Taylor return series is stationary (chang, 1998, p9)
When the time series do not have any form of trend and, therefore, some slow turning around point zero, we use the set of equations without the intercept term, we, therefore, use the t statistic associated with the ordinary least square estimates of the parameter under investigation. This is the dickey fuller t-statistic.
H0: Parameter under investigation = 0; the data needs to be differenced to ensure its stationarity
H1: Parameter under investigation < 0; the time series is stationary and therefore differencing is not necessary
At times, Dickey-Fuller procedure can be explained by the concept of a random walk.
2 Identify and estimate a suitable ARMA model for the three series.
Fitting of an ARMA model would necessitate the use of the Box –Jenkins methodology which has three steps; Model Identification, Model Validation, Model Estimation.
On Model identification, we would easily use act and pack plots of a time series data for instance if the ACF plots decay exponentially while the pacf plots cut off at some lag, p. We consider that process to be an Autoregressive process of the order of the cutting of lag i.e. ARMA(p,0), but if the pace plot decays exponentially while the acf cuts off after some particular lag then we consider that process as a moving average process of the order at the cutoff point.
Using these plots, we would, therefore, come up with very core and a series of possible candidate models to fit. Using these candidate models, we estimate model parameters as a key step in the whole methodology.
Using the fitted possible candidate models we use the Akaike Information Criterion (AIC) to validate the model adequacy; the model with the least Akaike Information Criterion is the best model.
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