I would like to implement an OLS with a sklearn.linear_model.LinearRegression.
I have a time series with 100 data points and the respective data.
My overall goal is to forecast the next 6 weeks. I have in x_train multiple explaining variables for my output. These include for example the date, the month and, amongst others, my lag variables. I have checked the significance of lags with the autocorrelation plot and it told me, lags 1-12 are significant, so 12 explaining variables are these 12 lags.
I have created 12 lag variables:
lag_variables=pd.concat([data.shift(1), data.shift(2),...., data.shift(12)]
These lag variables are 12 columns in my x_train dataframe, from which I choose my features.
However, if I want to forecast 6 data points, I need to update my lags.
Because for example for week 5, I don't have any lags 1-4, because I don't know them at the time of my forecast. For week 1 I know the lags 1-12, for week 2 I know the lags 2-12, and so on.
Python gives me now an error, since my x_train contains nan values, since I dont know all lags.
So my idea was, to forecast each week individually, so firstly I forecast week 1. Then, after I have forecasted week 1, I have the real value for week 1, and I can update my lags for week 2 with the real value. I am basically doing a rollig forecast with lags.
I have tried the following:
hist_x_train=[x for x in x_train]
hist_x_test=[x for x in x_test]
hist_y_train=[x for x in y_train]
hist_y_test=[x for x in y_test]
predictions=list()
for t in range(len(x_test)):
model=best_praams #gridsearch before the loop, chosses best parameter
model.fit(hist_x_train, hist_y_train)
y_pred=model.predict(hist_x_test[t])
predictions.append(y_pred)
hist_x_train.append(hist_x_test[t])
hist_y_train.append(y_pred)
print(y_test[t]) # this is my actual real value for that period; I don't
# know how to update this in x_train, so it shows up as a lag
Technically, the rolling forecast works like that if i don't have any lags in my x_train, but I don't know how to deal with the lags.
Can anyone please help me?
Thanks a lot!
Updating the train data with the predictions result in cascading errors which makes the next predictions almost constant or zero after some time, this should be avoided. Instead forecast for the next 6 weeks at one shot, or use multiple models (6 models here) to predict for the next 6 weeks, arrange your y_labels (y_1, y_2..... y_6) such that y_1 is lagged by 1 week, and y_2 by 2 weeks, and so on. and train then accordingly.
Related
I am looking to assess the accuracy of different classical time series forecasting models by implementing expanding window cross-validation with statsforecast on a time-series dataset with many unique IDs that have varying temporal lengths that can range between 1 to 48 months. I would like to forecast the next seven months after the ending month of each window and assess the accuracy with some error metric (e.g., sMAPE). There is potentially seasonality and trend in the different time series, so I would like to capture these in the cross-validation process as well. However, I am having difficulty and not fully understanding the different parameters (step_size, n_windows, test_size) in the package's cross-validation function.
Could someone advise me in setting up the right parameters? Is what I'm looking for even feasible with the function provided in the package? How do I decide the best value for step_size, test_size and n_windows?
For reference, my data looks like this:
df =
unique_id
ds
y
0
111111
2000-01-01
9
1
111111
2000-02-01
9
2
111111
2000-03-01
10
3
111111
2000-04-01
4
...
...
...
...
999999
111269
2003-10-01
32532
1000000
111269
2003-11-01
0
1000001
111269
2003-12-01
984214
And to be explicit, the history for individual unique_ids can vary (i.e., the length of the time series is unequal between unique_ids.)
I have already instantiated my StatsForecast object with the requisite models:
sf = StatsForecast(
df=df,
models=[AutoARIMA(season_length=12), AutoETS(error_type='zzz'), Naive()],
freq='MS',
n_jobs=-1,
fallback_model=Naive()
)
Then, I call the cross_validation method:
results_cv = sf.cross_validation(
h=7 # Predict each of the future seven months
step_size=?,
n_windows=?
)
I have tried an assortment of parameter values for step_size and n_windows together, and also just for test_size alone (e.g., 7 because I want to compare the last 7 months of actuals and forecasts in each window), but I'm always left with the following error:
ValueError: could not broadcast input array from shape (y,) into shape (z,)
I expect the end result to look similar to the data-frame presented in the statsforecast tutorial:
screenshot from the GitHub example
or scroll down to 'crossvaldation_df.head()'
Any pointers would be greatly appreciated. Thank you!
I have time-series sales data. First I group-by the sales by a year. Than I want to forecast the sales for the years 2021,2022 and 2023. I have data from the year 2000.
My question is similar to this one, however I want an answer on how to make forecast outside of the training index.
model = AutoReg(grp, lags=5)
model_fit = model.fit()
predictions = model_fit.predict(start=len(grp), end=len(grp)+3, dynamic=False)
If I do this the results are:
2021-12-31 NaN
2022-12-31 NaN
2023-12-31 NaN
2024-12-31 NaN
I can make it work if I set the end variable to len(grp)-1, but that means I am making predictions for data inside my sample I want to make predictions for the future.
The attribute dynamic seems salient as it says in the documentation it represents the index at which the predictions use dynamically calculated lag values.
The index of time-series did not have the freq set even though the index was annual.
grp.index.freq="Y"
Did the job for me. Also there does not appear to be any problem when you have numeric index of the time-series.
I have recently started using fbprophet package in python. I have monthly data for last 2 years and forecasting for next 9 months.
Since, I have monthly data I have only included yearly seasonality (Prophet(yearly_seasonality = True)).
When I plot components, trend values seem to be fine however, Yearly seasonality values are too high, I don't understand why?
Seasonality is showing 300 increase or -200 decrease. However, in actual graph it is not happening in any months in the past - what I can do to correct?
Code Used is as follows:
m = Prophet(yearly_seasonality = True)
m.fit(df_bu_country1)
future = m.make_future_dataframe(periods=9, freq='M')
forecast = m.predict(future)
m.plot(forecast)
m.plot_components(forecast)
There is no seasonality at all in your data. For there to be yearly seasonality, you should have a pattern that repeats year after year, but the shape of your time series from 10/2015 to 10/2016 is completely different from the shape between 10/2016 to 10/2017. So forcing a yearly seasonality is going to give you strange results, you should switch it off (i.e. just use Prophet's default settings).
There is an inconsistency in the seasonality factor of your data, there seems a little yearly seasonality between 2017-04 to 2018-10 . The first answer is absolutely true but incase if you feel there some seasonality you can reduce its impact by altering fourier order it has.
https://facebook.github.io/prophet/docs/seasonality,_holiday_effects,_and_regressors.html#fourier-order-for-seasonalities
This page has how to do so, the default fourier order is 10, reducing the values cahnges it effects.
Try this hope it helps you
I have a car speed dataset on a highway. The observations are collected at 15 min steps, which means I have 96 observations per day and 672 per week.
I have a whole month dataset (2976 observations)
My goal is to predict future values using an Autoregressive AR(p) model.
Here's my data repartition over the month.
In addition, here's the autocorrelation plot (ACF)
The visualization of the 2 plots above lead to think of a seasonal component and hence, a non-stationnary time series, which for me makes no doubt.
However, to make sure of the non-stationarity, I applied on it a Dickey-Fuller test. Here are the results.
Results of Dickey-Fuller Test:
Test Statistic -1.666334e+01
p-value 1.567300e-29
#Lags Used 3.000000e+00
Number of Observations Used 2.972000e+03
Critical Value (5%) -2.862513e+00
Critical Value (1%) -3.432552e+00
Critical Value (10%) -2.567288e+00
dtype: float64
The results clearly show that the absolute value of Test statistic is greater than the critical values, therefore, we reject the null hypothesis which means we have a stationary series !
So I'm very confused of the seasonality and stationarity of my time series.
Any help about that would be appreciated.
Thanks a lot
Actually, stationarity and seasonality are not controversial qualities. Stationarity represent a constancy (no variation) on the series moments (such as mean, variance for weak stationarity), and seasonality is a periodic component of the series that can be extracted with filters.
Seasonality and cyclical patterns are not exactly the same thing, but are very close. You can think as if this series in the images that you show can have a sum of sines and cosines that repeats itself for weekly (or monthly, yearly, ...) periods. It does not have any correlation with the fact that the mean value of the series seems to be constant over the period, or even variance.
My data: I have two seasonal patterns in my hourly data... daily and weekly. For example... each day in my dataset has roughly the same shape based on hour of the day. However, certain days like Saturday and Sunday exhibit increases in my data, and also slightly different hourly shapes.
(Using holt-winters, as I found discovered here: https://gist.github.com/andrequeiroz/5888967)
I ran the algorithm, using 24 as my periods per season, and forecasting out 7 seasons (1 week), I noticed that it would over-forecast the weekdays and under-forecast the weekend since its estimating the saturday curve based on fridays curve and not a combination of friday's curve and saturday(t-1)'s curve. What would be a good way to include a secondary period in my data, as in, both 24 and 7? Is their a different algorithm that I should be using?
One obvious way to account for different shapes would be to use just one sort of period, but make it have a periodicity of 7*24, so you would be forecasting the entire week as a single shape.
Have you tried linear regression, in which the predicted value is a linear trend plus a contribution from dummy variables? The simplest example to explain would be trend plus only a daily contribution. Then you would have
Y = X*t + c + A*D1 + B*D2 + ... F * D6 (+ noise)
Here you use linear regression to find the best fitting values of X, c, and A...F. t is the time, counting up 0, 1, 2, 3,... indefinitely, so the fitted value of X gives you a trend. c is a constant value, so it moves all the predicted Ys up or down. D1 is set to 1 on Tuesdays and 0 otherwise, D2 is set to 1 on Wednesdays and 0 otherwise... D6 is set to 1 on Sundays and 0 otherwise, so the A..F terms give contributions for days other than Mondays. We don't fit a term for Mondays because if we did then we could not distinguish the c term - if you added 1 to c and subtracted one from each of A..F the predictions would be unchanged.
Hopefully you can now see that we could add 23 terms to account for an shape for the 24 hours of each day, and a total of 46 terms to account for a shape for the 24 hours of each weekday and the different 24 hours of each weekend day.
You would be best to look for a statistical package to handle this for you, such as the free R package (http://www.r-project.org/). It does have a bit of a learning curve, but you can probably find books or articles that take you through using it for just this sort of prediction.
Whatever you do, I would keep on checking forecasting methods against your historical data - people have found that the most accurate forecasting methods in practice are often surprisingly simple.