Lecture 6: Modelling Volatility and Economic Forecasting
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- Опубліковано 5 сер 2024
- This is lecture 6 in my Econometrics course at Swansea University. Watch the lecture Live on The Economic Society Facebook page Every Monday 2:00 pm (UK time) between October 2nd and December 2017.
/ theeconomicsociety
In this lecture, I covered two topics: Modelling volatility and Economic Forecasting
Topic 1: Modelling Volatility
- Financial time series, such as stock prices, interest rates, foreign
exchange rates, often exhibit volatility clustering (periods of turbulence & periods of tranquillity).
- Various sources of news and other economic events may have an
impact on the time series pattern of asset prices; news can lead to various interpretations, and economic events like an oil crisis can last for some time. So we often observe the large positive and large negative observations in financial time series to appear in clusters.
- Such swings in oil prices and credit crises have serious effects. Investors are concerned about the rate of return on their investment, and the risk of investment and the variability or volatility of risk. Therefore, it is important to measure asset price and asset returns volatility.
A simple measure of asset return volatility is its variance over time. The variance by itself does not capture volatility clustering. It does not take into account the past history (time-varying volatility).
The ARCH Model:
- A measure that takes into account the past history (time-varying
volatility). In time series data involving asset returns, such as returns on stocks or foreign exchange, we observe autocorrelated heteroscedasticity.
Autocorrelated Heteroscedasticity:
- Heteroscedasticity, or unequal variance, in cross section data because of the heterogeneity among individual cross-section units. In time series data, we usually observe autocorrelation. In financial data, we observe autocorrelated heteroscedasticity (i.e., heteroscedasticity observed over different periods is autocorrelated). In the literature, this phenomenon called ARCH effect.
Drawbacks of ARCH Model:
- It requires estimation of the coefficients of p autoregressive terms, which consumes several degrees of freedom. It may be difficult to interpret all the coefficients, especially if some of them are
negative. The OLS estimating procedure does not lend itself to estimate the mean and variance function simultaneously. The literature suggests that any model higher than ARCH(3) is better
estimated by GARCH.
GARCH Model:
- Generalised autoregressive conditional heteroscedasticity. We modify the variance equation to get GARCH(1,1) by expressing the conditional variance at time t in terms of the lagged squared error term at time (t − 1), and the lagged variance term at time (t − 1).
- It can be shown that ARCH(p) model is equivalent to GARCH(1,1) as
p increases. In ARCH(p) we have to estimate (p + 1) coefficients, whereas in GARCH(1,1) model we estimate only 3 coefficients. GARCH(1,1) can be extended to GARCH(p,q) model (p lagged squared error terms, q lagged conditional variance terms). In practice, GARCH(1,1) has proved useful to model returns on financial assets.
The GARCH-M Model:
- Modify the mean equation by explicitly introducing the risk factor, the
conditional variance, to take into account the risk.
Topic 2: Economic Forecasting
- Based on past and current information, the objective of forecasting is to provide quantitative estimate(s) of the likelihood of the future
course of the object of interest (e.g. personal consumption expenditure). We develop econometric models and use one or more methods of forecasting its future course.
Methods of Forecasting:
- There are several methods of forecasting. We will consider three prominent methods of forecasting: 1. regression models, 2. autoregressive integrated moving average (ARIMA) models [Box-Jenkins (BJ) methodology], 3. vector autoregression (VAR) models (Sims).
Point & Interval Forecasts:
- In point forecasts we provide a single value for each forecast period. In interval forecasts we obtain a range, or an interval, that will include
the realized value with some probability. The interval forecast provides a margin of uncertainty about the point forecast.
ex post & ex ante
- Estimation period: we have data on all the variables in the model. Ex post forecast period: we also know the values of the regressand
and regressors (the holdover period - used to get some idea about the performance of the fitted model) Ex ante forecast we estimate the values of the depend variable beyond the estimation period but we may not know the values of the regressors with certainty.
Conditional & Unconditional Forecasts
- Conditional forecasts: we forecast the variable of interest conditional on the assumed values of the regressors. Recall that all along we have conducted our regression analysis, conditional on the given values of the regressors.
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I'm doing statistics but this best Econometrics presentation ever
Thank you very much, this is a quality lecture clearly explaining a complicated topic. It is a pleasure to listen to you teach.
Econometrics is scary for me. This is one of the best lecture I have ever seen. Excellent presentation. It's a request to upload more videos on time series and panel data modelling. I would love to learn from all of them.
Thank you so much. its a pleasure to listen to your teaching even though this was recorded 4 years ago.
Thank you so much sir ..really i have no words for ur way of teaching and explaning this ..after watching your vedeos made me happy and contended..thanks a lot ..your videos are just waoooo
Great lecture! Highly appreciated!
Thank you so much Sir ! I have been looking for volatility modelling concept hopelessly. Your lecture saved my thesis.
I am glad to know it helped.
Very good. Great presentation Dr Hanni, thank you a lot for the video. A wonderful lesson in econometrics , look forward to your next vedio.
Dahmani mohamed driouche thank you Dr. Dahmani for watching and for your kind words - such an honour. Thank you!
Thank you so much, very interesting, and I gained valuable knowledge on Time series data models.
fantastic presentation!
Dr you are great
Thanks professor this is a nice lecture
one more thing, I would like to know that, what is the economic meaning when the number if the lagged value of error variance becomes high. For example, is it meaningful to compare the ARCH (1) AND ARCH(8), especially the time measurement is the year?
great presentation and explanation !
Thanks for your comment.
nice
Excuse me Dr.. i need your help.. i want to make "exchange rate volatility variable".. some paper told me that i can use ARCH model.. in your presentation you use DLNEX.. does it mean Difference of LN exchange rate? Thanks from Indonesia..
thank you
Does this model apply for measuring volatility of gold? Plz do reply sir
Good presentation Dr. You should be in my university 😂😂
Thank you for your comment. I am glad to hear it helped.
Excellent lectures! I am studying for an exam on your videos! Could you also post the slides file?
Thank you for watching and for you comment. I am glad to know it helps. Lecture notes and datasets are available on my website Hanomics.com here is a link hanomics.com/mnm038/
I want to contact you regarding volatility modelling for my PHd thesis
thumbs up. sir lecture 2 of this series is not there.plz upload.
Muhammad Murtaza thanks for watching and for your kind comment. Lecture 2 was recorded audio only but I am still happy to share. Will upload it in the weekend.