Questions tagged [arima]

Refers to the AutoRegressive Integrated Moving Average model used in time series modeling both for data description and for forecasting. This model generalizes the ARMA model by including a term for differencing, which is useful for removing trends and handling some types of non-stationarity.

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12 views

What will be the value of AR and MA order? [duplicate]

I want to determine the value of p and q of ARIMA model from the ACF and PACF plot given bellow. What will be the order and why?
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19 views

Start and End time of time series objects [closed]

Im having some issues regarding calculation of my forecast accuracy. I think it's because I can't figure out how to specify the start of my time series. It's daily data of sold units. The data is ...
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Confused about Autoregressive AR(1) process

I create an autoregressive process "from scratch" and I set the stochastic part (noise) equal to 0. In R: ...
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21 views

Approximate ARMA model with high order AR model using AIC

There are many sources on why a "low-order" ARMA$(p,q)$ model (with small but non-zero $p,q$) can be expressed, theoretically, as an AR$(\infty)$ model (or an MA$(\infty)$ as well). For example this ...
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6 views

How to write out the model of a logarithmic SARIMA model

I have a model log(Z)~ARIMA(1,0,1)x(0,1,2) s=12, where Z is the series. In regular cases I would use the following method to write out the model. So in my case it would be $(1-\phi_1 B)(1-B^{12})...
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a general approach to derive state space representation from ARMA?

I see that the likes of this question has been asked many times but I'm just wondering whether there is a general approach to write ARMA models in state space representation? I have an exam in a few ...
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13 views

I need help to define which process this is [closed]

Which process is this? I already know that it's not an MA $σ_{t}^2= 0.01+0.7 ε_{t−1}^2$ connected with this process $y_{t}=0.5+0.5y_{t−1}+σ_tε_t$ thank you for your help
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1answer
38 views

Out-of-sample Rolling window forecast with ARIMA(0,0,0) with non-zero mean

I am doing a rolling window out-of-sample forecast and have fitted an ARIMA(0,0,1) model to a first difference time series. People argue that sometimes simpler models are better than more complicated ...
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1answer
22 views

Tentative ARIMA models for forecasting

I am doing out-of-sample forecasting with ARIMA and derived one model (0,0,1) with auto.arima on a differenced time series. The series is daily observations over the course of 3 years. I would like to ...
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33 views

ARIMA forecasting interpretation [closed]

Doing an out-of-sample forecast on sales data in r with an ARMA(0,0,1) model. The MA(1) coefficient is significant but has a value of -0.97 which is really close to the stationarity restriction. But ...
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18 views

Comparison of ARIMA and VAR accuracy

Can someone help explaining how to compare a forecast from an ARIMA model and a VAR model. I have tried calculating MAPE, MSE, RMSE etc. for my VAR forecast, but i simply cannot get it to work. ...
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1answer
28 views

Neural network vs SARIMA

In real-time data, sometimes you find that you cannot get a certain seasonality for the data because it is difficult to identify. This happens a lot in the prices of commodities and the stock market ...
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1answer
19 views

Choosing the train data size automatically - Sarimax Time Series Model

I am working on a forecasting application on some credit data. The flow of money looks as follows: I am using a sarimax model since I have weekly seasonality. For ...
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42 views

AIC vs. p-values for coefficients of an ARIMA model

Do the p values associated with ARIMA coefficients have any significance attached to them particularly when they are small? To be precise, can it happen that for an ARIMA(2,0,0) model the lag 2 ...
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11 views

Interpretation of the ACF of standardised residuals vs actual residuals

Is there any scientific reason why a lot of studies and packages choose the ACF plot of the standardised residuals rather than the residuals themselves?
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19 views

Are the forecasting methods like mean, naive, drift, weighted average applicable to non stationary time series?

Like AR, MA models essentially need the series to be stationary, do the other forecast methods mentioned above also follow stationary?
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What methods of forecasting should I be looking at to forecast sales?

I am wanting to forecast sales of different products within a business. I have a good background in mathematics (but mainly focused on analysis, group theory, algebra etc. as opposed to statistics). ...
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28 views

Does it make sense to fit an ARIMA model to the remainder component of a timeseries?

Suppose I have a timeseries, something like this: ...
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2answers
66 views

Why TBATS model giving poor result?

I have time series data of number of units ordered from a manufacturing plant and number of units delivered. The are multiple different plant sites for which I need to build forecasting models. I ...
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1answer
94 views

Time Series Forecasting - Daily data

I'm relatively new to time series forecasting. I've been assigned with the task of forecasting operation time of an industrial equipment based on a daily data (3 years of daily data). The prediction ...
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30 views

Guessing ARMA order just from the plot

I have this two plots, each one contains two realisations (orange/blue) of the same $ARMA(pi, qi)$ model. All orange instances share the same noise sequence $e_i$, and so do all the blue ones. I don'...
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1answer
50 views

forecast rainfall using ARIMA in R

I am a new student approaching ARIMA prediction analysis in R. If the question is too simple or incorrect, please forgive and guide me. I am currently using the ARIMA provided in R. I use the data as ...
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1answer
68 views

Help me about using ARIMA forecasting rainfall [closed]

I am currently using the ARIMA provided in R. I use the data as the rainfall time series in QuyNhon (Vietnam) from 2000 to 2017 to forecast rainfall for the next several years. I wish that the ...
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22 views

Negative coefficients of regressors in arimax,should be positive

I have two years of daily time series inbound call centers data starting from Jan 2018 to Nov 2019. I am doing arimax and regressors are mainly promotional flag along with day of the week (sun, mon ......
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1answer
32 views

ARIMA model for a single variable with hidden context

I have a signal which measures the power of a machine. I have been asked to fit an ARIMA model for this signal in order to find anomalies. However as far as I know, the power of the machine is ...
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19 views

Interpreting ARMA models?

After much searching I was able to picture in my mind an ARMA model with this analogy: AR representing the sales of a given item. MA representing a coupon given for the item. This analogy is given ...
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67 views

Kalman filter for AR(1) plus noise

I am working the following AR(1) plus noise state-space model $$ z_{t} = x_{t} + v_{t}\\ x_{t} = \phi x_{t-1} + c + w_{t} $$ Therefore, the transition matrix is $[\phi]$, the observation matrix is $[1]...
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Mann-Kendall Test of a trend

From the construction of Mann-Kendall Test, I conclude that in the absence of a trend, the data is supposed to be i.i.d. Therefore, one can not use Mann-Kendall Test to test trend in ARMA models. Is ...
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17 views

Forecasting method for different cohorts with large seasonal swings but otherwise stable data

I am attempting to forecast percentage of churn for different cohorts. However, I am unsure how to proceed after selecting an initial method. The churn is fairly stable except for large seasonal ...
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1answer
26 views

Inconsistent Ljung-Box test result and plot of autocorrelation function of residuals

I get an inconsistent result for the Ljung-Box test: in fact when I run it using the Box.test function it doesn't make me reject the null hypothesis of residuals being white noise, but when I plot the ...
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14 views

Forecast evaluation in ar model

I have to compare in R 3 autoregressive models I've previously identified and estimated.The comparison should be based on an out-of-sample prediction: using (T-R, in my case 216) observations to ...
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1answer
74 views

Parameter space restriction in random walk + noise model

Suppose we have a random walk + noise model so \begin{align} y_t & = \mu_{t-1} + \epsilon_t\\ \mu_t & = \mu_{t-1} + \eta_t \end{align} Then, it's straightforward to show that $$\...
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1answer
23 views

Estimate of an AR model

I have this part of a project which states this: Once you choose the best three models for each series (according to AIC, the PACF and ACF, and "from general to specific), the next step is to estimate ...
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3answers
83 views

Difference between MA and AR

I fail to see the difference between Moving Average (MA): $x_t=\epsilon_t+β_1\epsilon_{t−1}+…+β_q\epsilon_{t−q}$ Autoregressive (AR):   $x_t=\epsilon_t+β_1x_{t−1}+…+β_qx_{t−q}$ $x_t$ is ...
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25 views

Fitting the 'intercept only' regression model in Python

I am working on a project that includes time series forecasting and I decided to use ARIMA for this. Before determining p (AR order) and q (MA order), I need to run ADF test to determine the ...
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1answer
29 views

Anomaly detection using vector autoregression

I want to detect anomalies in multivariate time series using statistical approaches. In particular. I want to use a vector autoregression model like VAR, VARMA or VARIMA, to predict a time stamp $x_t$ ...
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Do these forecasts imply the ARIMA model is misspecified?

I have a time series of a stock return over more than 2 years. It's stationary (Augmented Dickey-Fuller test is significant). The plot looks like this: The ACF and PACF look like this: I think these ...
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1answer
70 views

How can I remove trend of model's forecast when I use ARIMA model?

I have to forecast future energy consumption. I decided to use ARIMA model. But my model's forecast shows the wrong trend. The blue line shows true value. And the orange line shows my model's forecast....
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1answer
42 views

Cointegration in ARIMAX regressions in R?

I’m running some ARIMA(X) regressions in R with several (control-) regressors including dummy variables and have some general questions concerning possibly cointegrated variables in ARIMA regressions. ...
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1answer
52 views

How to interpret the constant for an ARMA model

I'm trying to fit an ARMA(1,0) model for a timeseries that start at $10$ and drops slowly to $4$ in around $180$ steps. For this, I've tried to fit an ARMA model in python using the following: ...
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What are the necessary conditions so that the residuals of an ARIMA model behave as a normal distribution?

Simple and direct question I just had while implementing a solution: What are the necessary conditions so that the residuals of an ARIMA model behave as a normal distribution?
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1answer
141 views

Why is time series forecasting different for each software?

I have 2 different software programs: SPSS, and Statgraphics. I am using them for time series forecasting but Each one gives different arima parameters when using the auto ARIMA model, and The ...
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1answer
61 views

Differencing of AR(1) process

Let $z_{t}$ be stationary ARMA(p,q) (not ARIMA!) process. What would be the distribution of differencing of $z_{t}$? I mean the process $y_{t} = z_{t} - z_{t-1}$. My attempt: Let $z_{t}$ be ...
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1answer
64 views

I cannot understand formula for exogenous options in statsmodels' ARIMA

I need to use exogenous variables for my time series forecasting. And I found that I can include my exogenous variables into my ARIMA model using exogenous option. I want to know how this option ...
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54 views

Can I use ARIMA with hour data for two year prediction? [closed]

I am trying to use ARIMA model for time series forecasting. My data consists of hour by hour energy consumption. I have data for one year. So I have total 24*365 observations for energy consumption. ...
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1answer
40 views

95% prediction interval for an ARMA(2,2) model

What would the formula for a 95% prediction interval for an ARMA(2,2) model be? The specific model I am using is: an ARIMA(2,0,2) with non-zero mean, with the following parameter estimates: ...
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1answer
34 views

What is the correct model (AR, MA, or ARMA) and order for the data?

I am new to time series and forecasting and I have been assigned to determine the model and order for a data object. The ACF, PACF, and EACF are below: I was thinking it was an AR(1), but I am not ...
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1answer
42 views

Variance of AR(1) plus noise and its “equivalent” ARMA(1,1)

Let us consider the following state-space model $$ z_{t} = x_{t} + v_{t}\\ x_{t} = \phi x_{t-1} + w_{t} $$ where $ \phi< 1$, the errors $v_{t}\sim \mathcal{N}(0,V^{2})$ and $w_{t}\sim \mathcal{N}(0,...
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when fitting a regression model to a time-series, can I use lagged values of the time-series itself?

I'm fitting a regression model $y_t$ to a time series $x_t$ (not a dynamic model involving ARMA terms!). I saw that useful predictors to put in my model are $t$, seasonality variables and lagged ...
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1answer
15 views

when fitting a dynamic regression model to a TS, what would happen if we first fit a regression model and then fit an ARMA?

When fitting a dynamic regression model, we fit a model that has exogenous variables and also ARMA variables. What would happen if we first fit a regression of all exogenous variables, and then fit ...