Financial Econometrics (EF5070)

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Financial Econometrics (EF5070) 2023/2024 Semester A

Assignment 3

? The assignment is to be done individually.

? Your solution should consist of one single pdf file and one single R file.

? Clearly state your name, SIS ID, and the course name on the cover page of your pdf file.

? In your pdf file, indicate how you solved each problem and show intermediate steps. It

is advised to show numerical results in the form of small tables. Make your R code easyto-read. Use explanatory comments (after a # character) in your R file if necessary.

Overly lengthy solutions will receive low marks.

? You need to upload your solution (i.e., the one pdf file and the one R file) on the Canvas

page of the course (Assignments → Assignment 3). The deadline for uploading your

solution is 2 December, 2023 (Saturday), 11:59 p.m.

Financial Econometrics (EF5070) Dr. Ferenc Horvath

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Exercise 1.

The file a3data.txt contains the daily values of a fictional total return index.

? Calculate the daily non-annualized continuously-compounded (n.a.c.c.) net returns.

? Use the BDS test to determine whether the returns are realizations of i.i.d. random

variables.

? Plot the ACF of the returns and of the squared returns. Do these plots confirm your

conclusion which you obtained by using the BDS test?

? Based on the Akaike information criterion, fit an AR(p) model to the return time series

with ?? ≤ 5. Check whether the model residuals are realisations of a white noise or not

by plotting the ACF of the residuals and of the squared residuals, and by performing

the BDS test on the residuals.

? Perform the RESET test, Keenan’s test, Tsay’s F test, and the threshold test to determine

whether the daily n.a.c.c. net returns indeed follow an AR(p) model, where p is equal

to the number of lags which you determined in the previous point based on the Akaike

information criteria. Is your conclusion (based on the four tests) regarding the validity

of an AR(p) model in accordance with your conclusions regarding whether the residuals

in the previous point are realisations of a white noise?

? For each daily n.a.c.c. net return, create a dummy variable which takes the value 1 if

the return was positive and the value zero otherwise. Build a neural network model

where

o the output variable is the previously created dummy variable,

o the two input variables are the previous day’s n.a.c.c. net return and its

corresponding dummy variable,

o there is one hidden layer with three neurons,

o the two input variables can enter the output layer directly by skipping the

hidden layer,

o and the activation functions are logistic functions.

o Train the neural network using the daily n.a.c.c. net returns, but do not use the

last 1000 observations.

o Using the last 1000 observations, forecast the signs of the next-period returns.

Determine the mean absolute error of your forecast. (I.e., in how many percent

of the cases did your model correctly forecast the sign of the next-period return

and in how many percent of the cases did it make a mistake in forecasting the

sign?)

Financial Econometrics (EF5070) Dr. Ferenc Horvath

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Exercise 2.

The file HSTRI.txt contains the Hang Seng Total Return Index (which is the major stock market

index of the Hong Kong Stock Exchange) values from 3 January, 1990 to 22 September, 2023.

? Calculate the daily non-annualized continuously-compounded (n.a.c.c.) net returns.

? For each daily n.a.c.c. net return, create a dummy variable which takes the value 1 if

the return was positive and the value zero otherwise. Build a neural network model

where

o the output variable is the previously created dummy variable,

o the two input variables are the previous day’s n.a.c.c. net return and its

corresponding dummy variable,

o there is one hidden layer with three neurons,

o the two input variables can enter the output layer directly by skipping the

hidden layer,

o and the activation functions are logistic functions.

o Train the neural network using the daily n.a.c.c. net returns, but do not use the

last 1000 observations.

o Using the last 1000 observations, forecast the signs of the next-period returns.

Determine the mean absolute error of your forecast. (I.e., in how many percent

of the cases did your model correctly forecast the sign of the next-period return

and in how many percent of the cases did it make a mistake in forecasting the

sign?) Is this result in accordance with the Efficient Market Hypothesis,

according to which (roughly speaking) returns are not predictable?

Financial Econometrics (EF5070) Dr. Ferenc Horvath

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Exercise 3.

Consider again the daily n.a.c.c. net returns from Exercise 2.

? Calculate the standard deviation of the first 7324 returns.

? Create a dummy variable for each observed return such that the dummy variable takes

the value of 1 if the absolute value of the return is greater than the previously

calculated standard deviation and it takes the value of zero otherwise.

? Build a neural network model where

o the output variable is the previously created dummy variable,

o the two input variables are the previous day’s n.a.c.c. net return and its

corresponding dummy variable,

o there is one hidden layer with three neurons,

o the two input variables can enter the output layer directly by skipping the

hidden layer,

o and the activation functions are logistic functions.

o Train the neural network using the daily n.a.c.c. net returns, but do not use the

last 1000 observations.

? Using the last 1000 observations, forecast whether the absolute value of the nextperiod return will be higher or not than the earlier calculated standard deviation.

Determine the mean absolute error of your forecast. (I.e., in how many percent of the

cases was your model forecast correct and in how many percent of the cases was it

incorrect?) Is this result in accordance with the concept of volatility clustering?

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