GARCH – Tutorial and Excel Spreadsheet

This article gives a simple introduction to GARCH, its fundamental principles, and offers an Excel spreadsheet for GARCH(1,1).Scroll down to the bottom if you just want to download the spreadsheet, but I encourage you to read this guide so you understand the principles behind GARCH.

Least squares is a fundamental concept in statistics, and is widely used across many fields, including engineering, science, econometrics, and finance. Least squares determines how a dependent variable changes in response to the variation of another variable (call the independent variable).

The difference between the actual and the predicted value is known as the residual.  Fitting a modeling involves minimizing the sum of the squares of the residuals.

The least squares approach assumes that the squared error has the same magnitude across the entire data set.  This assumption is known as homoskedasticity.  But financial data (known as a time series) has periods of high and low volatility, with periods of high volatility often clustering together.  This is known as heteroskecadicity.

In reference to modeling fitting, this means the residuals vary in magnitude.  Volatility clustering means the data is auto correlated.  GARCH is a statistical tool that helps predict the residuals in k data

ARCH means Autoregressive Conditional Heteroskedasiticy and is closely related to GARCH. The simplest method to predict stock volatility is an n day standard deviation, and let’s consider a rolling year with 252 trading days.  If we want to predict stock prices for the next day, the mean is usually a safe starting point.

But the mean treats each day with the same weight.  Giving the recent past more significance is more logical, with perhaps an exponential weighted average being a better method to predict tomorrow’s stock price.

However, this method does not capture any data older than a year, and the weighting is rather arbitrary.  The ARCH model, however, varies weights on each residual such that the best fit is obtained.  The GARCH (General Autoregressive Conditional Heteroscedasiticy) is similar, but gives recent data more significance.

The GARCH(p,q) model has two characteristic parameters; p is the number of GARCH terms and q is the number of ARCH terms. GARCH(1,1) is defined by the following equation.

GARCH equation

h is variance, ε is the residual squared, t denotes time. ω, α and β are empirical parameters determined by maximum likelihood estimation. The equation tells us that tomorrow’s variance is a function of

  • today’s squared residual,
  • today’s variance,
  • the weighted average long-term variance

GARCH(1,1) captures only once square residual and one square variance.

This is not a magic wand, and financial analysts should be use the approach with a high degree of caution.  Given the appropriate circumstance, the predicted variance can greatly differ from the actual variance. Techniques such as the Ljung box text are used to determine if any autocorrelation remains in the residuals.

Several researchers have highlighted deficiencies in GARCH(1,1) models, including its failure to predict the volatility in the S&P500 more accurately than other methods.

GARCH in Excel

This Excel spreadsheet models GARCH(1,1) on time series data. You can use your own data, but the spreadsheet uses the GBP/CAD exchange rate between May 2007 and October 2011 (data obtained using this Forex data downloader spreadsheet).  The spreadsheet uses Excel’s Solver for the maximum likelihood estimation, but full instructions are given on its use.

General Autoregressive Conditional Heteroscedasiticy

Download Excel Spreadsheet for GARCH(1,1) analysis


26 thoughts on “GARCH – Tutorial and Excel Spreadsheet

  1. hello
    I would really like to understand step by step how to build a model garch
    I have much need for my thesis.
    I understand that I take a data column
    a column yields
    and then??
    please help me

  2. i will used the A-DCC GARCH model for my thesis. unfortunately, i have zero knowledge on the econometric and time series analysis. i hope anybody can help me to understand the model.

    1. Not sure if I understand your question. You get the alpha,beta and omega values through model fitting with Excel’s Solver (everything’s already set up in the spreadsheet)

      1. I have the same question. Can’t understand how you calculated the alpha,beta and omega values. Can you please provide with a step by step process to compute those values?

  3. Hey I wondered why do you use difference (B14-B13) and not return LN(B14/B13) when estimating the volatility. Can`t see you get the right implied volatility using difference. But when calculating the implied volatility I changed B collum to use return so the data will be I(0). Get insanly high implied volatility using difference hence the data will probably not be I(0) when using difference. could be that you forgot to divede with B13 when making the sheet? ((B14-B13)/B13) which is almost the same as LN(B14/B13). Best regard Bengt-Rune

  4. Hello Samir,
    Have read this with great interest.
    Am I correct in saying that to solve the spreadsheet, i.e calculate h(t+1) and calculate the predicted variance for the next time period, you would use from the spreadsheet cells:

    B5+(B6*D1279)+(B7*B4) or .00008615

    Thanks
    Lynn

    1. Hi Lynn,

      Have you got an answer on your question? Is it alright to use cell “B4” (h at time t) as your variance?

      Thanks,

      Shu

  5. Hi Samir,

    Your explanations on GARCH, VaR, etc using excel are very very helpful for someone with limited knowledge on finance.

    I have a question on calculation of “log likelihood function.” What is the interpretation of the calculation (i.e. =LN((1/SQRT(2*3.1415927*F15))*EXP(-0.5*D15/F15)))? If you can guide me to a reference, I would appreciate it.

    Kind regards,

    Shu

  6. Hi! Im not sure how you calculated the ω, α and β values. I am using daily PSEi data from the years 1994-2011.

  7. Hi! I’m not sure how to calculate OMEGA, ALPHA and BETA values. I’m using SENSEX and net FIIs data for the past 10 years.

  8. I believe this is how you would find the variables (Omega, Alpha and Beta):
    use solver as follows: set objective ( Cell G1281) to Max by changing variable cells (B5:B7)
    The idea is find the variables that maiximize the likelihood

  9. How would I calculate the significance and standard errors of the Arch and Garch coefficient in this model on excel?

  10. Hi, I was wondering how would you work out the standard errors and thus the significance of alpha and beta in excel. I am trying to analyse whether the arch and garch effects in my model are significant for explaining the evolution of volatility of stock market returns in Japan

  11. Pls, i am working on a project titled impact of oil price volatility on exchange rate in nigeria. But my supervisor said i should use garch model to capture the volatility. Pls, i need a person to help me out

  12. Hi,
    i am working on impact of financial derivatives on volatility and for that i need to build GARCH model. Please tell me step by step. And also tell me about Eviews software. I am using NSE data.

  13. Thank you for providing this example! Your example helped me figure out how to set up a worksheet to estimate recursive econometric models.

    Very much appreciated!!

  14. hi can you tell me how you get the alpha, beta and omega in the model and how can you explain the result which you got from the Excel sheet. thank u

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