Generating random samples from ARIMA(p,d,q) model

Katatonia Sh

unread,

Mar 18, 2021, 7:19:20 AM3/18/21

to pystatsmodels

I wanna generate samples from ARIMA(p,d,q) in Python, but I could not find any method to this. There is a method to generate samples ARMA(p,q) but not ARIMA.

Moreover, how is it possible to generate samples with an initial value? For example, in the current model, samples start from 0 but I want to generate samples starting at 50.

Regards

jseabold

unread,

Mar 18, 2021, 9:46:23 AM3/18/21

to pystatsmodels

On Thursday, March 18, 2021 at 6:19:20 AM UTC-5 katato...@gmail.com wrote:

I wanna generate samples from ARIMA(p,d,q) in Python, but I could not find any method to this. There is a method to generate samples ARMA(p,q) but not ARIMA.
Moreover, how is it possible to generate samples with an initial value? For example, in the current model, samples start from 0 but I want to generate samples starting at 50.

I believe you can use the unintegrate functions for this.

In [276]: from statsmodels.tsa.arima_model import unintegrate, unintegrate_levels

In [277]: from statsmodels.tsa.arima_process import arma_generate_sample

In [278]: y = arma_generate_sample([1, -.2, -.1], [1, .7], nsample=1000)

In [279]: levels = [50]

In [280]: unstationary_y = unintegrate(y, levels)

In [281]: ARIMA(y, order=(2, 0, 1), trend='c').fit().summary()

Out[281]:

"""

SARIMAX Results

==============================================================================

Dep. Variable: y No. Observations: 1000

Model: ARIMA(2, 0, 1) Log Likelihood -1394.270

Date: Thu, 18 Mar 2021 AIC 2798.540

Time: 08:41:11 BIC 2823.079

Sample: 0 HQIC 2807.866

- 1000

Covariance Type: opg

==============================================================================

coef std err z P>|z| [0.025 0.975]

------------------------------------------------------------------------------

const 0.0471 0.072 0.654 0.513 -0.094 0.188

ar.L1 0.2572 0.059 4.354 0.000 0.141 0.373

ar.L2 0.0264 0.049 0.540 0.589 -0.069 0.122

ma.L1 0.6636 0.048 13.887 0.000 0.570 0.757

sigma2 0.9509 0.045 21.368 0.000 0.864 1.038

===================================================================================

Ljung-Box (L1) (Q): 0.00 Jarque-Bera (JB): 1.56

Prob(Q): 0.99 Prob(JB): 0.46

Heteroskedasticity (H): 0.94 Skew: 0.06

Prob(H) (two-sided): 0.58 Kurtosis: 2.85

===================================================================================

Warnings:

[1] Covariance matrix calculated using the outer product of gradients (complex-step).

"""

In [282]: ARIMA(unstationary_y, order=(2, 1, 1), trend='t').fit().summary()

Out[282]:

"""

SARIMAX Results

==============================================================================

Dep. Variable: y No. Observations: 1001

Model: ARIMA(2, 1, 1) Log Likelihood -1394.270

Date: Thu, 18 Mar 2021 AIC 2798.540

Time: 08:41:28 BIC 2823.079

Sample: 0 HQIC 2807.866

- 1001

Covariance Type: opg

==============================================================================

coef std err z P>|z| [0.025 0.975]

------------------------------------------------------------------------------

x1 0.0471 0.072 0.654 0.513 -0.094 0.188

ar.L1 0.2572 0.059 4.354 0.000 0.141 0.373

ar.L2 0.0264 0.049 0.540 0.589 -0.069 0.122

ma.L1 0.6636 0.048 13.887 0.000 0.570 0.757

sigma2 0.9509 0.045 21.368 0.000 0.864 1.038

===================================================================================

Ljung-Box (L1) (Q): 0.00 Jarque-Bera (JB): 1.56

Prob(Q): 0.99 Prob(JB): 0.46

Heteroskedasticity (H): 0.94 Skew: 0.06

Prob(H) (two-sided): 0.58 Kurtosis: 2.85

===================================================================================

Warnings:

[1] Covariance matrix calculated using the outer product of gradients (complex-step).

"""

Katatonia Sh

unread,

Mar 18, 2021, 1:03:10 PM3/18/21

to pystatsmodels

Thank you so much.

I checked the results and there are some negative values. These time-series samples correspond to demand which should be non-negative. Is it possible to generate TS with non-negative values? In addition, is it possible to generate TSs which fall in an interval [l,u]?

What does "unintegrate" do in your code? I would be thankful if you can give me a reference on math behind generating these samples.

Regards

Skipper Seabold

unread,

Mar 18, 2021, 9:38:27 PM3/18/21

to pystat...@googlegroups.com

On Thu, Mar 18, 2021 at 5:03 PM Katatonia Sh <katato...@gmail.com> wrote:
> I checked the results and there are some negative values. These time-series samples correspond to demand which should be non-negative. Is it possible to generate TS with non-negative values? In addition, is it possible to generate TSs which fall in an interval [l,u]?

Hmm. Nothing obvious comes to mind but I don't have a deep intuition about this.

I guess you'll have to calibrate the parameters for the simulated
values and/or play with the level value. Maybe clip the series with
some noise, if you don't really care about the ARMA parameter values.

> What does "unintegrate" do in your code? I would be thankful if you can give me a reference on math behind generating these samples.

It's what we use to forecast ARIMA models from differenced series.

https://github.com/statsmodels/statsmodels/blob/6d4d588b00547296f678af2e8de8bf3bbea1102e/statsmodels/tsa/tsatools.py#L758

> --
> You received this message because you are subscribed to the Google Groups "pystatsmodels" group.
> To unsubscribe from this group and stop receiving emails from it, send an email to pystatsmodel...@googlegroups.com.
> To view this discussion on the web visit https://groups.google.com/d/msgid/pystatsmodels/8fe73c58-2786-4854-8cf2-ad88b23ea449n%40googlegroups.com.

Reply all

Reply to author

Forward