How to generate equeation from the coefficients?

[newuser_01]

Hi,

I don't know much about ARMA but hoping that one of you can help me understand this. I calculate the coefficients from timeseries but how can I can calculate the equation from the timeseries?

I've the
1. coefficients, std. error, t-statistics, prob. of
c (constant)
AR(1), AR(2), AR(3), AR(4), AR(5)
MA(1), MA(2), MA(3), MA(4)

and
2. R-squared, Adjusted R-squared, S.E. of regression, Sum squared, log likelihood, Mean dependent var, S.D. dependent var, Akaike info criterion, Schwarz criterion, Durbin-Watson stat

and

3. Inverted AR-roots, Inverted MA-roots


How can I calculate the equeation from here.. Based on these values if I write an equation then I'll be able to estimate the tomorrow's value. This is probably a dummy question for most of you..

[EViews Gareth]

I don't understand your question.

[newuser_01]

I've a time series.

And calculated all these coefficients using the tool. But I don't have the equation.

If this was a linear equation then it might look like:

y = 2x + 3


So now I want to write the same for this non linear equation.

y = m*(y-1) + r*(y-2) + c etc... so I'm after something like this.

[EViews Gareth]

You mean you just want to know how to include ARMA terms in an equation? Just add AR(1) as a regressors or MA(1)

[startz]

Or if what you're trying to do is forecast tomorrow's value, push the forecast button in the equation window.

[newuser_01]

something like that, let me clarify my questions again, let's say i have the following time series

t value
1 55
2 54
3 53
4 52
5 51
6 50
7 49

t is time.. value is the value... If I calculated ARMA stuff from this series and ended up with the following info:

1. coefficients, std. error, t-statistics, prob. of
c (constant)
AR(1), AR(2), AR(3), AR(4), AR(5)
MA(1), MA(2), MA(3), MA(4)
and
2. R-squared, Adjusted R-squared, S.E. of regression, Sum squared, log likelihood, Mean dependent var, S.D. dependent var, Akaike info criterion, Schwarz criterion, Durbin-Watson stat
and
3. Inverted AR-roots, Inverted MA-roots

And now I would like to write and equation for time (8) because I know the data up to 7, and will write the equation and then based on that I want to be able to calculate the value at 8. While doing that I will probably you the value at 7, 6, 5, 4, etc..

so if my value is y(t) the equation will look like

y(t) = q*(y(t-1) + y(t-2) + y(t-3)) + c etc.. it can be different than this but I don't know how to write this equation using the coefficients I have, can you give me an example.

You might say

y(t) = AR1 * y(t-1) + AR2 * y(t-2) - MA1 * y(t-1) ....

Hope it is clear now..

[newuser_01]

yes i would like to forecast tomorrow's value but I am not interested in the value, I would like to have the equation.

[startz]

If y_t is the variable and we call e_t the error term, the equation is something like

Code: Select all

y_t = ar(1)*y_(t-1) + ar(2)*y_(t-2) + e_t +ma(1)*e_(t-1)

[newuser_01]

Thanks for the response, I understood all excep the error term, which one is the error term?

Code: Select all

y_t = ar(1)*y_(t-1) + ar(2)*y_(t-2) + e_t +ma(1)*e_(t-1)

I guess with the constant (i.e. c) my equation will look like:

Code: Select all

y_t = c + ar(1)*y_(t-1) + ar(2)*y_(t-2) + e_t +ma(1)*e_(t-1)

I've the following info but I don't know which one is the error term, and I don't have individual error term for each item:

1. coefficients, std. error, t-statistics, prob. of
c (constant)
AR(1), AR(2), AR(3), AR(4), AR(5)
MA(1), MA(2), MA(3), MA(4)
and
2. R-squared, Adjusted R-squared, S.E. of regression, Sum squared, log likelihood, Mean dependent var, S.D. dependent var, Akaike info criterion, Schwarz criterion, Durbin-Watson stat
and
3. Inverted AR-roots, Inverted MA-roots

Thanks

[startz]

e_t is the error term.

You might want to do some background reading on regression models in general and ARMA models specifically. Understanding how error terms fit in is central to anything you want to do with these equations.

[newuser_01]

Thanks for the response, can you recommend something to read one error terms? I think it is called white noise.. and can you let me know whether I can calculate the error terms from the data I have?
Thanks

[startz]

Look at the Regression Analysis article on Wikipedia, particularly the section Linear Regression

[newuser_01]

ok thanks, i will have a look, what about my second question:

Can error term (e(t), e(t-1)) be calculated from the data I have:

I have the time-series and the estimations and
1. coefficients, std. error, t-statistics, prob. of
c (constant)
AR(1), AR(2), AR(3), AR(4), AR(5)
MA(1), MA(2), MA(3), MA(4)
and
2. R-squared, Adjusted R-squared, S.E. of regression, Sum squared, log likelihood, Mean dependent var, S.D. dependent var, Akaike info criterion, Schwarz criterion, Durbin-Watson stat
and
3. Inverted AR-roots, Inverted MA-roots

Can error term (white noise) be calculated from these?

[newuser_01]

Please see my question below, does anyone know how to calculate the error term (i.e. white noise) from the listed data I have?

ok thanks, i will have a look, what about my second question:

Can error term (e(t), e(t-1)) be calculated from the data I have:

I have the time-series and the estimations and
1. coefficients, std. error, t-statistics, prob. of
c (constant)
AR(1), AR(2), AR(3), AR(4), AR(5)
MA(1), MA(2), MA(3), MA(4)
and
2. R-squared, Adjusted R-squared, S.E. of regression, Sum squared, log likelihood, Mean dependent var, S.D. dependent var, Akaike info criterion, Schwarz criterion, Durbin-Watson stat
and
3. Inverted AR-roots, Inverted MA-roots

Can error term (white noise) be calculated from these?

[startz]

Look up "RESID" or "residuals" in the help system.