Model of the US Economy: CointegratedVARModelHandbook

[ac_1]

x{1}+y{1}-z{1}

and

x{1}-y{1}

are your error correction terms. For DET=RC, you include constants in those. (Can be different for each of the two, but has to be the same in all locations for a given ECT). For DET=RTREND, you include constant and trend in those with the same requirement.

Thanks.

In DET=RC I have included a constant in EACH error correction term.

In DET=RTREND I have included a constant and a trd in EACH error correction term. Should set trd = t be scaled? Attached is 4) DET=RTREND, I cannot seem to include both the CONSTANT and trd variables in EQUATION.

Also, in comparing all 4 DET's what should I be expecting from the plots and ECT's?

[TomDoan]

Yes. You want a coefficient on the trends. As written, the trend is going to be outsized compared to the other movements.

The estimated ECT with DET=RTREND has the TREND as the fourth variable, not CONSTANT.

What you see will depend upon the numbers that you put in. DET=RC would have the variables generally having different levels. DET=TREND would have trending series (not necessarily the same trends---depends upon the drift values that you include). DET=RTREND would have series which seem to differ by a trend (though with two ECT's, it gets complicated---you might want to put the restricted trend only into one of the two terms).

[ac_1]

Hi Tom,

I'd like to confirm the following w.r.t. updating a quarterly VAR-MACRO model.

If I have data from FRED and
- GDPC1 which is quarterly, with
- other macro monthly series

I would update at the end of the 1st quarter 2025 i.e. MARCH 2025 using the 'last' monthly data, having lagged 1 quarter for GDPC1 (reason being GDPC1 final estimate for 2024:4 is released 2025:1 i.e. on 27th March 2025).

Correct?

Code: Select all

*===============================
cal(q) 1947:1
allocate 2025:1

data(format=fred) / GDPC1
data(format=fred,compact=last) / UNRATE

set LGDPC1 = GDPC1{1}

* transformations
set grgdp = 100.0 * ((LGDPC1/LGDPC1{4}) - 1.0)

What if I included FEDFUNDS, which is 'averages of daily figures'.

Would the quarterly model still be practical/viable for forecasting from 2025:2 multi-step ahead, as I would have
- grgdp (lagged 1 quarter),
- 'last' values for UNRATE, and other macro monthly series, for the quarter,
- and then there would be the 'averages of daily figures’ for FEDFUNDS for the last month of the quarter.


thanks,
Amarjit

[TomDoan]

I would generally recommend having quarterly series that are relatively close to having the same "timing". GDP as a flow variable, is already, in effect, an average of daily figures. It sounds like you would have FedFunds the same way, so doing the URATE as quarterly averages rather than final month would make more sense.

[ac_1]

I would generally recommend having quarterly series that are relatively close to having the same "timing". GDP as a flow variable, is already, in effect, an average of daily figures. It sounds like you would have FedFunds the same way, so doing the URATE as quarterly averages rather than final month would make more sense.

Thanks. So, I would remove compact=last, as compact=[average] is the default, from monthly macro series. And for e.g. inflation calculate y/y from the average quarterly price levels series. Thus, I would be forecasting quarterly averages, all variables, multisteps ahead.

And backtest OOS results would be more focused on loss measures, rather than direction, e.g. using daily data on a financial series in an upwardly trending market I would want to be predicting upward movements as well as being 'close' to the actual.

Right?

[TomDoan]

I would generally recommend having quarterly series that are relatively close to having the same "timing". GDP as a flow variable, is already, in effect, an average of daily figures. It sounds like you would have FedFunds the same way, so doing the URATE as quarterly averages rather than final month would make more sense.

Thanks. So, I would remove compact=last, as compact=[average] is the default, from monthly macro series. And for e.g. inflation calculate y/y from the average quarterly price levels series. Thus, I would be forecasting quarterly averages, all variables, multisteps ahead.

Correct.

And backtest OOS results would be more focused on loss measures, rather than direction, e.g. using daily data on a financial series in an upwardly trending market I would want to be predicting upward movements as well as being 'close' to the actual.

Close doesn't necessarily mean correct sign. If the actual is small positive, small negative would generally be seen as more accurate than large positive. You can use an asymmetrical loss function which has a higher penalty on wrong signs but that would still see small negative as more accurate than large positive---it would just change the interpretation of "large" vs "small".