# SNARIMAX SNARIMAX model. SNARIMAX stands for (S)easonal (N)on-linear (A)uto(R)egressive (I)ntegrated (M)oving-(A)verage with e(X)ogenous inputs model. This model generalizes many established time series models in a single interface that can be trained online. It assumes that the provided training data is ordered in time and is uniformly spaced. It is made up of the following components: - S (Seasonal) - N (Non-linear): Any online regression model can be used, not necessarily a linear regression as is done in textbooks. - AR (Autoregressive): Lags of the target variable are used as features. - I (Integrated): The model can be fitted on a differenced version of a time series. In this context, integration is the reverse of differencing. - MA (Moving average): Lags of the errors are used as features. - X (Exogenous): Users can provide additional features. Care has to be taken to include features that will be available both at training and prediction time. Each of these components can be switched on and off by specifying the appropriate parameters. Classical time series models such as AR, MA, ARMA, and ARIMA can thus be seen as special parametrizations of the SNARIMAX model. This model is tailored for time series that are homoskedastic. In other words, it might not work well if the variance of the time series varies widely along time. ## Parameters - **p** *Type* → `int` Order of the autoregressive part. This is the number of past target values that will be included as features. - **d** *Type* → `int` Differencing order. - **q** *Type* → `int` Order of the moving average part. This is the number of past error terms that will be included as features. - **m** *Type* → `int` *Default* → `1` Season length used for extracting seasonal features. If you believe your data has a seasonal pattern, then set this accordingly. For instance, if the data seems to exhibit a yearly seasonality, and that your data is spaced by month, then you should set this to 12. Note that for this parameter to have any impact you should also set at least one of the `p`, `d`, and `q` parameters. - **sp** *Type* → `int` *Default* → `0` Seasonal order of the autoregressive part. This is the number of past target values that will be included as features. - **sd** *Type* → `int` *Default* → `0` Seasonal differencing order. - **sq** *Type* → `int` *Default* → `0` Seasonal order of the moving average part. This is the number of past error terms that will be included as features. - **regressor** *Type* → `base.Regressor | compose.Pipeline | None` *Default* → `None` The online regression model to use. By default, a `preprocessing.StandardScaler` piped with a `linear_model.LinearRegression` will be used. ## Attributes - **differencer** (`Differencer`) - **y\_trues** (`collections.deque`) The `p` past target values. - **errors** (`collections.deque`) The `q` past error values. ## Examples ```python import datetime as dt from river import datasets from river import time_series from river import utils period = 12 model = time_series.SNARIMAX( p=period, d=1, q=period, m=period, sd=1 ) for t, (x, y) in enumerate(datasets.AirlinePassengers()): model.learn_one(y) horizon = 12 future = [ {'month': dt.date(year=1961, month=m, day=1)} for m in range(1, horizon + 1) ] forecast = model.forecast(horizon=horizon) for x, y_pred in zip(future, forecast): print(x['month'], f'{y_pred:.3f}') ``` ```text 1961-01-01 494.542 1961-02-01 450.825 1961-03-01 484.972 1961-04-01 576.401 1961-05-01 559.489 1961-06-01 612.251 1961-07-01 722.410 1961-08-01 674.604 1961-09-01 575.716 1961-10-01 562.808 1961-11-01 477.049 1961-12-01 515.191 ``` Classic ARIMA models learn solely on the time series values. You can also include features built at each step. ```python import calendar import math from river import compose from river import linear_model from river import optim from river import preprocessing def get_month_distances(x): return { calendar.month_name[month]: math.exp(-(x['month'].month - month) ** 2) for month in range(1, 13) } def get_ordinal_date(x): return {'ordinal_date': x['month'].toordinal()} extract_features = compose.TransformerUnion( get_ordinal_date, get_month_distances ) model = ( extract_features | time_series.SNARIMAX( p=1, d=0, q=0, m=12, sp=3, sq=6, regressor=( preprocessing.StandardScaler() | linear_model.LinearRegression( intercept_init=110, optimizer=optim.SGD(0.01), intercept_lr=0.3 ) ) ) ) for x, y in datasets.AirlinePassengers(): model.learn_one(x, y) forecast = model.forecast(horizon=horizon) for x, y_pred in zip(future, forecast): print(x['month'], f'{y_pred:.3f}') ``` ```text 1961-01-01 444.821 1961-02-01 432.612 1961-03-01 457.739 1961-04-01 465.544 1961-05-01 476.575 1961-06-01 516.255 1961-07-01 565.405 1961-08-01 572.470 1961-09-01 512.645 1961-10-01 475.919 1961-11-01 438.033 1961-12-01 456.892 ``` ## Methods > [!NOTE] > > **forecast** > > Make a forecast at each step of the given horizon. > > **Parameters** > > - **horizon** — `int` > - **xs** — `list[dict] | None` — defaults to `None` > [!NOTE] > > **learn\_one** > > Update the model. > > **Parameters** > > - **y** — `float` > - **x** — `dict | None` — defaults to `None` ## References - [ARMA - Wikipedia]() - [NARX - Wikipedia]() - [ARIMA - Forecasting: Principles and Practice]() - [Anava, O., Hazan, E., Mannor, S. and Shamir, O., 2013, June. Online learning for time series prediction. In Conference on learning theory (pp. 172-184)]()