SARIMA model order - time-series

I am using SARIMA model (1,1,1)(2,1,1,96) for a dataset with ACF and PACF plots as follows:
ACF plot of the dataset
PACF plot of the dataset
After using the mentioned model, I look into the ACF and PACF plots to make sure that I have covered all the dependencies; however, the ACF and PACF plots show a large value at lag 96. I would appreciate it if I get some help about the modifications that I should make to my SARIMA model order. Please consider that my data has a daily seasonality and since it is 15 min data, S=96.
ACF and PACF plots after fitting the model
Thank you,

You can use auto_arima function in pmdarima package to iterate over combinations of orders and get the best value based on AIC score.You have identified seasonal and non-seasonal orders looking at acf and pacf plots.You can use those orders as starting parameters.
import pmdarima as pm
from sklearn.metrics import mean_squared_error
model = pm.auto_arima(<train_data>,error_action="ignore", suppress_warnings = True,
seasonal = True,
m = 96,
start_p = 1,start_q = 1,d=1,
start_P = 2,start_Q = 1,D=1,
max_p = 12,max_q = 12,max_d=2,
max_P = 4,max_Q = 4,max_D = 2,
test='adf', #use adf test
information_criterion='aic', #AIC or BIC
stepwise = False, trace = False)
After that you can get the model diagnostics using plot_diagnostics function
model.plot_diagnostics(figsize=(8,8))
also you can get the Ljung-Box and Jarque-Bera statistics from summary function to check the distribution of residuals and correlation of residuals.
model.summary()

Related

XGBoost feature importance (TFIDF + TruncateSVD)

I have an XGBoost model that runs TFIDF vectorization and TruncateSVD reduction on text features. I want to understand feature importance of the model.
This is how I process text features in my dataset:
.......
tfidf = TfidfVectorizer(tokenizer=tokenize)
tfs = tfidf.fit_transform(token_dict)
svd = TruncatedSVD(n_components=15)
temp = pd.DataFrame(svd.fit_transform(tfs))
temp.rename(columns=lambda x: text_feature+'_'+str(x), inplace=True)
dataset=dataset.join(temp,how='inner')
.......
It works okayish and now I'm trying to understand importance of the features in the dataset. I generate the charts using:
xgb.plot_importance(model, max_num_features=15)
pyplot.show()
And get something similar to:
this chart
What would be the right way to "map" importance SVD dimensions to the dimensions of the initial dataset? So I know importance of summary and not summary_1, summary_2, summary_X.
Thanks
one thing you can try is getting the how important each original feature is to creating new features. you can get it using the following:
feature_importance_scores = np.abs(svd.components_).sum(axis=0)
feature_importance_scores /= feature_importance_scores.sum() # normalize to make it more clear
you can get the overall importance by multiplying these values with xgb.feature_importances_

Facing difficulty in understanding Trend, Seasonality and Residual graph?

I am forecasting the new covid cases in upcoming time and I want to see the trend, seasonality present in the dataset.
I tried to see the trend and seasonality using seasonal decompose.
from statsmodels.tsa.seasonal import seasonal_decompose
#decomposition
decomposition = seasonal_decompose(x = df.new_cases,
model = 'multiplicative')
decomposition.plot()
and I got this -
I am not able to understand the seasonal graph. What does it trying to show? Does that mean my dataset doesn't has any seasonality?
and what does Resid graph indicates?

Trend and Seasonality from time series

how can we extract trend, seasonality from a time series in a way SARIMAX does internally.
I need to use the same to understand how much importance (feature importance) trend, seasonality, AR component, MA component and exogenous variables are to the forecast.
You can do this way -
from statsmodels.tsa.seasonal import seasonal_decompose
#decomposition
decomposition = seasonal_decompose(x = df.y, model = 'multiplicative')
decomposition.plot()
# df is the dataframe of y is the name of column having values of which you want
to see trends and seasonality.
# model value can be additive or multiplicative.

Reproduce ARIMA Forecast (Pandas)

I am quite new to the ARIMA model, and I have a question on how to analyze the chart of the ACF (autocorrelaction function) according to the lag. Is it correct to take into account the ACF value of 0.5 which corresponds to about 450 lag and then set the arima model on these values?
This is my graph:
and this is my simple code for arima model:
import from statsmodels.tsa.arima_model import ARIMA
# fit model
model = ARIMA(df['valore'], order=(400,1,0))
model_fit = model.fit(disp=0)
print(model_fit.summary())
# plot residual errors
residuals = DataFrame(model_fit.resid)
residuals.plot()
pyplot.show()
residuals.plot(kind='kde')
pyplot.show()
print(residuals.describe())
Thanks!
P.S. my page in jupyter format and the data (csv) can be found at: github
In theory it is possible to include an order of 400 in an ARIMA model. In practice that value is astronomically high for an ARIMA model (Anything higher than 3 or 4 is considered unusual in an ARIMA model). I would double check your data and also double check how you are calculating the ACF.
Additionally the p order of the ARIMA(p,d,q) model is usually determined using the PACF, not the ACF. You use the ACF for determining q.

Time Series forecasting using caret package in R

I am trying to forecast using caret package on economic data. Is there any method to predict values for next coming years?
library(mlbench)
library(caret)
library(pROC)
library(caTools)
library(ROCR)
myTimeControl <- trainControl( method = "timeslice", initialWindow = 36,
horizon = 12, fixedWindow = FALSE, allowParallel = TRUE, classProbs = TRUE,
summaryFunction = twoClassSummary, verboseIter = TRUE)
modelRF <- train(
as.factor(class) ~ . , data = TestData, method = "rf", metric = "ROC",
ntree = 1000, preProc = c("center", "scale"), trControl = myTimeControl)
Please help me to predict the class for next coming years.
You'll need to use the predict method with the x data for what you want to predict.
For forecasting time series, first consider that your time series is a regression problem then you can use extreme gradient boosting method which is a time taking model but its accuracy is very good. I have applied many model for time series forecasting like ARIMA, PROPHET, HOLT WINTER'S, EXPONENTIAL SMOOTHING, etc but my forecasting accuracy is best in extreme boosting method although it's a regression model.
train(QTY~BILLDATE1,
data = train1,
method = "xgbDART",
preProc = c("center", "scale"))
Tree based models tend to be weak predictors of time indexed economic data. They have some success in panel data. You will be better using support vector machines or LSTM's for time indexed economic forecasts.

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