Recalculate fitted values/Simulate of an Arima model with different xreg values

Question

I have about 100 ARIMA models, where each models the demand of a separate household using the temperature as an exogenous value. I've used the auto.arima from the forecast package on R and used xreg to input the temperature.

Now I changed/simulated several series of temperature values and want to use the new temperature values to recalculate the demand using the previously constructed ARIMA model.

I think I can calculate the values manually by referring to each coefficient value of the model. However, it will be inefficient as I have more than 100 models.

Is there a more efficient way to get this done?

So far my code is

arima_model = 
    auto.arima(sqrt(house_data$demand), 
    xreg = as.matrix(house_data$temp)) 
    # model for demand
temp_auto_arima = auto.arima(house_data$temp) 
    # model for the temperature
new_temperature = simulate(temp_auto_arima) 
    # simulate temperature to get a new series

What do you mean by 'I have 100 models'? Did you use 100 different models on the same data? — Sextus Empiricus, Apr 29 '22 at 12:42
"...want to use the new temperature values to recalculate the demand..." You changed the temperature (the regressor) to recalculate the demand. This is unclear to me. How do you calculate the demand? Isn't the demand a given/observed variable that you do not calculate. Or are you talking about making predictions for some other situation? — Sextus Empiricus, Apr 29 '22 at 12:44
@SextusEmpiricus I have 100 models each for a separate household — Thusitha Thilina Dayaratne, May 02 '22 at 01:02
I want to simulate the demand value based on the temperature change (and the already constructed ARIMA model) — Thusitha Thilina Dayaratne, May 02 '22 at 01:03
What do you mean by inefficient? Are you referring to a way to tell simulate (from the forecast package?) new xreg values? — Sextus Empiricus, May 02 '22 at 06:10
I mean recalculation of demand values with simulated temperature manually, which is inefficient as I have more than 100 models — Thusitha Thilina Dayaratne, May 02 '22 at 06:22
So you want to make less models? You want a way to have it not done manually? What do you mean by 'manually'? — Sextus Empiricus, May 02 '22 at 06:30
No, I want to recalculate the demand values with simulated temperature values and the constructed Arima models — Thusitha Thilina Dayaratne, May 02 '22 at 06:34
But where is the problem? Is the problem in the way that you implement it in code, is the writing of the code inefficient? Or is the problem in having to do a lot of computations, is the algorithm inefficient? So, are you looking for a different code or a different algorithm? — Sextus Empiricus, May 02 '22 at 06:43
I'm just wondering whether is there any function that I can directly use to recalculate the demand values without doing it manually — Thusitha Thilina Dayaratne, May 02 '22 at 06:45
What are you doing manually now? You are already using the function simulate which does it automatically for you. — Sextus Empiricus, May 02 '22 at 06:46
that is to simulate different temperatures. I want recalculate the household demand values using the simulated new temperature — Thusitha Thilina Dayaratne, May 02 '22 at 06:47

Sextus Empiricus · Answer 1 · 2022-05-02T14:09:53.027

1

You can use simulate(arima_model, xreg = new_x) with a the parameter xreg to simulate a time series with a different regressor vector or matrix.

Below is an example

### generate data
set.seed(1)
t = c(1:1000)
x = sin(t/1000*2*pi*3)
noise = arima.sim(n = 1000, list(ar = c(0.2,-0.5), ma = c(1,0.5)),
                  sd = 0.1)
plot time series
demand = x + noise
plot(t,demand, 
     main = "black: original model \n red: simulate(mod, xreg = new_x)")
model time series and plot newly generated series
arima_model  = auto.arima(y, xreg = x)
new_x = sin(t/10002pi*3+pi)
points(t,simulate(arima_model , xreg = new_x), col = 2)
mod

edited May 02 '22 at 14:09

answered May 02 '22 at 07:17

Sextus Empiricus

77,915

@Thusitha Was this the issue? Or do you not want to change the noise in the newly simulated demand time series and only change the time but keep the same arima noise? – Sextus Empiricus May 02 '22 at 07:21
Thank for the answer. However, what I want to do is instead of simulating the demand arima model, recalculate the demand values using the model with simulated temperature – Thusitha Thilina Dayaratne May 02 '22 at 07:43
I don't want to simulate the demand. I simulate the temperature and want to use that temperature to calculate the demand using the already constructed ARIMA model – Thusitha Thilina Dayaratne May 02 '22 at 07:46
@ThusithaThilinaDayaratne the model is not recalculated, with simulate you use the already constructed arima model (the estimated parameters). Only the particular realization of the noise terms are recomputed/resimulated. Is that what you mean by 'I don't want to simulate'? – Sextus Empiricus May 02 '22 at 08:09
@ThusithaThilinaDayaratne if you show the manual method then it becomes clear what you want to do. – Sextus Empiricus May 02 '22 at 08:13
I'm referring to manually calculate as in https://stats.stackexchange.com/questions/266967/manual-calculation-of-arima1-1-0-forecast – Thusitha Thilina Dayaratne May 03 '22 at 10:41
if I use simulate function, it simulates the demand. But instead of simulating the demand, I want to only simulate the temperature and then use that to calculate demand values using the obtained ARIMA model – Thusitha Thilina Dayaratne May 03 '22 at 10:42

Recalculate fitted values/Simulate of an Arima model with different xreg values

1 Answers1

plot time series

model time series and plot newly generated series