Questions tagged [forecasting]

Prediction of the future events. It is a special case of [prediction], in the context of [time-series].

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30 views

Problem with ets function diagnostic for model with trend and seasonality

I have been meaning to fit an exponential smoothing model to a monthly series that looks like the one below: When I decompose the series it is almost evident that we have seasonality and also there ...
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23 views

Two charts with regular peaks and troughs but only one is stationary?

I'm reading Forecasting Principles and Practice section on stationarity. We are shown the following image and asked which are stationary: Obvious seasonality rules out series (d), (h) and (i). Trends ...
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Multivariate ARIMA model with irregular time-series

I have a financial time-series dataset consisting of prices of 12 different products (financial futures contracts) that expire x months away from now. So if I plot these 12 contracts with end-of-day ...
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Manually calculations of MA(3) model differs from the results of Arima values using the forecast Package

I have a time series that was fitted to a MA(3) using the forecast package in R. ...
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11 views

Breakdown and interpret the ARIMA model

Electricity usage goes up during winter because heating is used Electricity usage goes up during summer because air conditioner used. $$y^*_t = \beta_1x^*_{1,t} + \beta_2x^*_{2,t} + \eta_t,$$ $$(1-\...
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14 views

Interpreting ACF and PACF for data which have had its seasonality removed

I'm currently working on a project and trying to figure out how to interpret my ACF and PACF plots. I have removed seasonality from the data in order to establish the trend, now when plotting my ACF ...
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1answer
45 views

How to bootstrap time series data

I have this dataset that contains multiple series (50 products). My dataset has 50 products (50 columns). each column contains the monthly sales of a product. I recently learned about bootstrap and ...
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23 views

Determine when a value has stabilized

Q: Given a set of data points, what is the best way to determine when the value has stabilized? I have sales data for multiple products since their launch and want to find the place where their demand ...
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1answer
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SARIMAX statsmodels model_fit.forecast predicts NaN values after 52

I have a dataset of bike renting between 2014 and 2020, and I want to use data between 2014 and 2018 to predict future usage, and to test it on 2019. However when using predict, I get Nan values after ...
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Why are my forecast intervals so large? (ARIMA)

I am trying to perform a forecast on jet fuel prices (from FRED), where i total 260 observations running from jan. 2000 to august 2021 with monthly frequency and no apparant seasonality From looking ...
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Evaluating Probabilistic/Bayesian Forecasts - PIT Values & How to Generate

Suppose you are modelling a linear regression $y_i = \alpha + \beta x_i + \epsilon_i$, in probabilistic terms: $$ \mu_i = \alpha + \beta x_i, $$ $$ y_i \sim \mathcal{N}(\mu_i, \sigma). $$ For each ...
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Meaning of Diebold-Mariano (DM) test for other accuracy measures (MDA, $R^2$...)

I am trying to compare the accuracies of two time series forecasts. I read about the Diebold-Mariano (DM) Test, which tests the null hypothesis of $E[d_t]=0$, where $d_t=g(e_{it})-g(e_{jt})$ is the ...
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27 views

Prediction of MA(1) process

Let $X_t = Z_t +\theta Z_{t-1}$, invertable, $Z_t\sim WN(0,\sigma^2)$. Consider the prediction $P_nX_{n+1} = \phi_{n1}X_n + ... + \phi_{nn}X_1$. Derive the coefficients $\phi_{n1},...\phi_{nn}$. My ...
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Forecast of stationary sequence [closed]

Today my professor left us with this task: Let $\{X_t\}$ be a stationary sequence with mean $\mu$ and covariance $r(\cdot)$. Using prediction equations derive the coefficients $a$ and $b$ prediction $...
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Time Series Forecasting with known values

Is there a way to incorporate known values into a time series model? For example if we look at hotel bookings. It makes sense to build a seasonal forecasting model, but I'd like to try to factor in &...
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PC-Vector Autoregression (PC-VAR)

When using PC-VAR model for forecasting purposes, can we define it in the following manner? where a k-dimensional vector of intercepts is denoted by φ0 , Φ represents a k × k matrix of coefficients ...
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23 views

Error in forecasting using ARIMA with multiple regressors

I'm trying to do a multivariate time series forecasting using dynamic regression. The data was collected for 148 weeks with two main variables- Shipment Qty(dependent variable) and Net.Production.Qty(...
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Can you generate output for ICE plot?

I am looking for multi-step forecast deterministically with a random forest. I am aware the random forest isn't the best model for multi-step forecasting however I need to do it for comparison reasons....
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19 views

Forecast with inputs that are previous forecasts

I have an hourly time series and I have built a linear regression model that has different inputs: Previous value of the time series. Value in the last period of the time series, it is a weekly ...
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30 views

Can TBATS be used in the case of deterministic seasonality?

I have a monthly dataset which consist of 176 points. I validated that it is stationary by adf.test and it has deterministic seasonality by ...
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1answer
44 views

Forecasting with log transformed data and then taking the exponential of my predictions [duplicate]

I am aware a similar question was asked here Interpreting forecast predictions of log transformed data. But I would like a deeper comment/answer. I have a time series and want to make forecast. I ...
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Is there a smoothing technique taking account of covariates?

Hypothetical scenario: (Just to explain my needs. Maybe not meaningful in reality) Suppose we have recorded $\{y_{ij}\}_{i=1}^{n_j}$, the annual consumption expenditure per capita for $n_j$ households ...
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45 views

How to select P and Q in ARIMA

I am new to using ARIMA and I would like to know how to determine the p, q values of ARIMA by PCF and PACF. Here is the raw data figure. The raw data is a human glucose data collected.The blue data is ...
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26 views

SAS: Flat line forecast ARIMA model?

I'm trying to forecast a large dataset using ARIMA (The data does not have seasonality), I ended up getting an ARIMA(2,1,2) model where the log of volume was taken due to increase in variance over ...
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How can I reduce the propagation of errors in multi-step time series forecasting?

I have a multi-step forecasting task where I am predicting values $H$ hours in the future. Supposing that the forecast issue is done at time t, I will produce predictions for the next $H$ hours: $\{\...
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1answer
40 views

Forecasting Multi-variate data using Arima errors with Fourier terms and covariate on a weekly data in R

I'm planning to do a multivariate time series forecasting using arima errors with fourier terms. Data assumptions-moderate seasonality. one independent variable(x) and dependent variable(y) Weekly ...
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SARIMA Equation interpretation

I'm building a SARIMA model in Excel, but I'm not sure if I follow the deffinition with Lag operators $L^n$. For a $SARIMA(p, d, q)(P, D, Q)_m$ model, are the following equations right? $$\Delta_{m}^{...
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Auto. Arima and ARIMAX for multi variate time series forecasting

I'm trying to do multivariate time series forecasting using the forecast package in R. The data set contains one dependent and independent variable. From the cross-correlation the 0 day lag of the ...
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Large dataset time series model help!

I'm doing a time series project on quite a large data set based on the stocks of a company over time. The first image shows quite a large increase in variance over time and suggests the series isn't ...
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36 views

ARIMAX and auto.arima for multivariate time series forecasting in R

I'm trying to do multivariate time series forecasting using the forecast package in R. The data set contains one dependent and independent variable. From the cross-...
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14 views

Differences between Static Factors, Dynamic factors and Exploratory factor analysis in Time Series

I came across many types of factor analysis techniques in the context of time series data. I am not sure whether exploratory factor analysis refers to the same static factor analysis methodology. If ...
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23 views

Can log-transform to TS reduce forecast accuracy vs non-transformed TS

I have to apply a SARIMAX model to over 300 TS. Many of them have increasing volatility which can be addressed by aplying log to the TS. Problem is that also many TSs don't have this problem. Is it ok ...
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1answer
27 views

Should boostrapped prediction intervals be normally distributed?

I am trying to implement boostrap prediction interval example of FPP3 book in python for learning purposes (https://otexts.com/fpp3/prediction-intervals.html). Prediction interval is estimated by ...
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14 views

Forcasting Daily Data with End of the Month Pattern

I was hoping I could get some guidance on a forecasting problem that I am working on. I have data with a daily frequency & I have a number of time series that follow very distinct patterns. For ...
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19 views

Forecasting average of two time series: Group Input vs Output

I'm trying to get the average movement of a 1-step-forecast of $n$ time series with a SARIMA model. Some series have good fit, but others don't. What is a better approach: Make a new Time Series that ...
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auto.arima with xreg in-sample performance worse than univariate

Based on this discussion ARIMAX vs. Regression With ARIMA Errors and the blog post link https://robjhyndman.com/hyndsight/arimax/ , I have tried the following: ...
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45 views

Does this ARIMA model take seasonality into account?

I'm writing a tutorial on traditional time series forecasting models. One key issue with ARIMA models is that they cannot model seasonal data. So, I wanted to get some seasonal data and show that the ...
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32 views

Supply chain planning - multiple warehouses

I work in retail company, we have multiple warehouses across the Europe, we sell a lot of different articles. In supply chain planning we take article, forecast sales of it (ARIMA) and in next step we ...
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18 views

Why does the RMSE stay the same regardless of the algorithm that I use?

I have a dataframe with users, items, and ratings that are either 0 or 1. There are more items than users, some users might rate lots of common items, and some not any common items at all. Here is a ...
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25 views

Combining Linear Regression and Exponential Smoothing

I am working on a forecasting model that predicts inventory levels of a certain item based on how far behind our production line is predicted to be on a given day. EDA showed a high level of ...
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15 views

Forecasting using PC-VAR

I am trying to forecast an index by using a PC-VAR. When performing the PCA, can I exclude the response variable from the dataset and find the PCs and later build a VAR with the response variable and ...
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1answer
45 views

Sales forecasting. What model to choose and how to interpret ACF/PACF?

I have the following raw sales timeseries: Clearly it's not stationary since it does have somewhat of an increasing trend (non-stationarity also verified by DF-test). By differencing I obtain the ...
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Measuring similarity between students to build an exam recommender system

I am playing around with the following problem: I have various groups of students from various schools and they receive online questions. A group receives the same questions, but different groups in ...
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Time Series Forecasting Within a Year + Trends From Past Years

I'm trying to wrap my head around the following time series forecasting problem: My goal is to forecast revenue/expenditure within a fiscal year based on daily data Daily data include cumulative ...
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32 views

Which one should we use for forecasting: differenced series and cox-box transformed series?

I have a non-stationary dataset which shows the prices. I wanted to apply time series analysis on it. I took the first differences of the dataset and it became stationary. Then I determined the p and ...
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27 views

How to interpret ACF/PACF plots with no recent lag correlations?

I have a time-series data that looks like this: There is obviously an upward trend in this data, so I do differencing with lag of 1, i.e., Series = Y(t) - Y(t-1) The differenced series looks as ...
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How can I fix this error in computing accuracy when training an LSTM for time series forecasting

I'm trying some simples scenarios for getting familiar with time series forecasting with LSTM using Keras. I've created a very simple time series, which is a linear decaying function from N (100000) ...
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7 views

Exogenous Variables in SARIMAX

I am trying to make a SARIMAX model. The data has loan type (A,B,....F), loan duration with several groups, and loan amount (y-variable). From that, I generated dummy columns for each categories from ...
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1answer
22 views

Why forecast accuracy is very high in Restricted VAR but not in individual OLS estimate?

When a VAR is estimated and tested on the test data the RMSE of the model was around 25. However when I estimated a restricted VAR by setting coefficients of the lagged terms of the dependent variable ...
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1answer
13 views

Forecasting volatility from serially uncorrelated (squared) returns

I am trying to estimate future volatility based on historical stock price data, using (G)ARCH models. I have computed the ACF and PACF of returns and squared returns, and none of them show signs of ...

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