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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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Strange rugarch error: $ operator invalid for atomic vectors? [on hold]

So, I am trying to make a huge nested for loop (optimizations be left for later) to fit all of the GARCH models available from rugarch. This is my MLE that ...
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Proof expression for the autocovariance function of AR(1)

The representation for the model AR(1) is the following: $Y_t=c+ϕY_{t-1}+ε_t$ where $c=(1-ϕ)μ$ ($c$ is a constant). I want to understand the calculations that there are behind the general formula ...
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Why would you introduce a constant in a moving average model, when you already have the option of differencing?

In the online forecasting book of Hyndman (https://otexts.com/fpp2/MA.html) firstly the use of differencing is explained. After that he shows the formula for a moving average model: $$y_t = c + \...
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Mean of an ARMA(1,1) model

Let $X_t$ be a weak stationary process ARMA(1,1) $X_t=c+\phi X_{\left(t-1\right)}+\theta\varepsilon_{\left(t-1\right)}+\varepsilon_t$ $\varepsilon_t$ ~ $WN\left(0,\sigma^2\right)$ The estimated ...
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51 views

Converting MA(1) to AR(p)

While it is $MA(1)$ process there is no dependence between $u(t)$ and $u(t-1)$ i.e $$u(t)=v(t)+Q(1)v(t-1)$$ but when i converted it to AR process i get $u$’s that is dependent on the other $u$’s i.e. $...
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Principles behind time-series forecasting intervals

So, this is truly a bit of a general question, but I am not aware of the guiding principles (if there are any) behind forecasting intervals. For whatever time-series model one might be using, whether ...
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Predict variables for urban growth model [on hold]

perhaps some people can help me. I am working on an urban growth model for a local council. I have a VERY large number of lot (property) scale variables of various types (census, property value, sale ...
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MA Residuals in R using arima()

I fit a MA(1) model using arima() in R: set.seed(100) y = arima.sim(list(ma=c(-.6)),n=100) fit=arima(y, order=c(0,0,1), include.mean = FALSE) The model being fit ...
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Trouble when using Dates imported from MySQL to R in order to use ARIMA [on hold]

long time lurker, first time poster. I've recently been digging into time-series analysis and, for my master thesis one of the steps is to use an ARIMA model to be able to forecast short-term taxi ...
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37 views

ARIMAX - predict

I have the monthly number of patients in a psychiatric facility from Jan 2010 to Dec 2018 - the data shows a seasonal pattern. I want to forecast the number of patients in the facility from Jan 2019 ...
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48 views

Predicting Building Fire Alarms

I have Building fire-alarm data for around 6 months - Date and the no. of building fire alarms triggered for that Date. I have to forecast the no. of fire alarms that can trigger in future based on ...
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39 views

How to fit a stepwise regression with ARIMA errors using Arima function in R?

I am fitting a regression model with ARIMA errors in R using the Arima function from the ...
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8 views

Stationarity with some disruptive values

I have a time series with a huge disruption in a pair of its values, which if I understand well makes squared residuals not independent. The ADF test suggests the process is stationary, and there ...
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how can i convert a data frame of multiple stocks data (historical stock prices, country, sector) to time series [on hold]

how can i deal/ read the csv file with a horizontal time series data, but there are a different categories for every stock and ticker as well. the header of the columns include ticker, country, ...
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Does it make sense to run a SARIMA model and then a ARCH(0,0)-GARCH(1,1) model on residuals?

It was tough to write the question in a simple manner. A time series I am working with follows a seasonal ARIMA model. In my software I cannot jointly estimate a SARIMA and a GARCH(1,1) model. Is it ...
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Difference between ACF of the sample & ACF of the residuals + interpretation of the diagnostics

I'm new to this topic but, since my book is not very helpful, I consulted different sites about this argument before creating this question, like: READING ACF AND PACF PLOTS Interpret the partial ...
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How do you express ARIMA(2,1,2) in terms of the backshift operator?

I've so far achieved the following: $$y_t-y_{t-1}=\phi_1y_{t-1}+\phi_2y_{t-2}- \theta_1e_{t-1}-\theta_2e_{t-2}+e_t$$ Therefore Yt-BYt=(phi)Byt+phiB^2yt-B(theta)et-B^2(theta)et+et Yt-BYt-(phi)Byt-...
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When we are proving why ARIMA(0,1,1) is equal to simple exponential smoothing, why can we considered theta to be equal to (1-alpha)

I know this is a very basic question, but its not clarified within my lectures. Essentially when you have ARIMA(0,1,1) You can simplify the theta 1 term in order to obtain SES via stating its (1-...
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Returns correlated, but squared returns not correlated

I'm trying to apply a GARCH model to a financial time series, and as usual I plotted the ACF and PACF of both returns and squared returns. In my time series the returns show serial correlation, but ...
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Which are the benefits of using ARIMA vs LSTM for time series forecasting? [duplicate]

I have already read this question: https://datascience.stackexchange.com/questions/12721/time-series-prediction-using-arima-vs-lstm but I want to know in which circumstances is better ARIMA and in ...
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25 views

AIC values for auto.arima [closed]

I have a problem with identifying why auto.arima suggest specific coefficients. I have time series with multiple seasonalities and I am trying to forecast future values using STL+ARIMA. I have been ...
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Model time series as real-valued or integer-valued?

I have a positive-valued time series of daily prices (a sample is listed below -- there are a few thousand observations) that is recorded to two decimal places. It is stationary after computing the ...
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How do I prove that ARIMA(0,1,1) is equivalent to simple exponential smoothing?

this is an exam question of mine, but I am really struggling with it. I have seen proofs online but they are too vague and do not connect the dots explicitly. Would someone be able to post a proof ...
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AR(1)-GARCH(1,1). A bad fit with log likelihood?

Consider these two DCC models: ...
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Determine paramaters for SARIMA model

I have the following timeseries with a frequency of 12 (months). Since there is both a trend and seasonality, I differenced the timeseries. To determine the parameters p, q, P and Q for the SARIMA(p, ...
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ARIMA model with measurement error

I'm interested in forecasting a time series $m_t$ which is contaminated with measurement error $e_t$, so the observed time series is $y_t = m_t + e_t$. I can suppose $m_t$ and $e_t$ are independent ...
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ARMA process forecasts and maximum likelihood parameters

I have some trouble understanding the forecasting/inference process of ARMA models. From Hamilton (which I am reading now), we can obtain forecasts at $Y$ from any linear process with r.v. values $X$...
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ARIMA lag order selection by auto.arima

I use the funtion auto.arima in my dataset auto.arima(Clean_Ts_Dados,trace = T, stepwise = F, approximation = F) and got ...
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Time series models (e.g. ARMA) a type or extension of GLM? Particular/stipulated forms of dependence in time series models

I am trying to understand the relationship between ARMA Time Series models and the GLM (Generalized Linear Model) family of models. As far I know, all GLMs have the following 3 components: 1) random ...
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Variance inhomogeneity in time series when forecasting

I am using a time series for monthly temperatures to predict future temperatures. To this I am using the seasonal ARIMA model and Holt Winters forecast, and my results seems fine. However, my data ...
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Calculate ARIMA fitted value by hand

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33 views

Covariance non-zero mean AR(1)

Why when I compute the autocovariance function of a non-zero mean AR(1), X(t)-u=Φ(X(t-1)-u)+ε the presence of the mean does not change my result and so the formula should be the same of a zero-mean ...
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Proof that sequential GARCH fitting is not efficient?

I've read that authors like Tsay (as well as several other researchers) use a sequential method for fitting a ARCH-type model. This means first estimating the conditional mean model (ARMA-type) and ...
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AR & MA order from the ACF & PACF plots

I am running a TS model & below are my ACF & PACF plots... In theory if the ACF plot is significant after Pth lag & PACF shows some geometric decay we can infer it is a MA series but my ...
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Compute forecasts and 90% forecast intervals for ARIMA(p,1,q) models

Consider the two models (ARIMA(1,1,0) and (ARIMA(0,1,1)):
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Choosing daily seasonal ARIMA model order vs. auto.arima

I have the following output_ts that looks like this: When I run unit root tests, I receive the following output seeming to indicate that my series is trend ...
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Estimating a MS-ARMA(p,q)-GARCH(r,s) parameters via MCMC

I am currently working on a MS-ARMA-GARCH model proposed by Dhiman das on this paper, and trying to fit it on simulated data. So far I understand the model and its construction, but I'm having a hard ...
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How to obtain an HP filter trend less susceptible to end-point bias?

My understanding is that if a series is stationary, using the HP filter on it does not introduce cyclical artifacts. Also, it has been proposed that in order to overcome the end-point bias one can use ...
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Returns forecast back to closing price?

I'm working with log returns. I've selected an ARMA-GARCH for mean and volatility forecasting and I would like to get the forecasted confidence intervals and plot expressed in terms of the closing ...
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What causes the degeneration of correlation in a simulated time series?

I am trying to simulate an ARMA(1,1) process with the following characteristics: $\phi$ = 0.97 $\theta$ = 0.80 Standard deviation $s$ = 245 Mean $m$ = 1000 ...
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Factorised form of Autoregressive Polynomial

I'm new to Time Series Analysis. I've read that when inverting autoregressive characteristic polynomial of arbitrary finite degree, we need to write it in its factorized form: $$\phi_p(x) = \prod_{i=1}...
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Does R's arima() fit / use multiplicative or additive seasonality?

I have searched Cross Validated and read the documentation of the stats package in R, but I cannot figure out, whether the arima() implementation uses additive or ...
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What is the relationship between the prediction interval of an ARIMA(p,d,q) and the prediction interval of the original variable

The title may be enough, I want to know what is the relationship between the prediction interval of an ARIMA(p,d,q) and the prediction interval of the original variable. Lets say that d = 1, so that I ...
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38 views

Error in the standard deviation when simulating an ARMA(1,1) using arima.sim

I'm trying to simulate an ARMA(1,1) process whose autoregressive and moving average parameters are, respectively, 0.74 and 0.47. Moreover, I want the simulated data to have mean equal 900 and standard ...
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An alternative to seasonal analysis in ARIMA models (SARIMA)?

I recently became aware of a property of time series with which I was previously unfamiliar: that a finite-dimensional autocovariance function is equivalent to an infinite-dimensional power spectrum, ...
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Stationarity in a ARIMA Model with External Regressors

I have a question about when we apply an ARIMA model with external regressors. Just a quick note of my understanding on the topic, an ARIMA model with external regressors is when we apply a Regression ...
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1answer
43 views

Forecast for ARIMA in R doesn't seem to fit

I've been trying to implement some ARIMA modelling of data in R (haven't been using R for long so not sure how well this is done), using the forecast library, but the forecasting part itself doesn't ...
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ACF and PACF of residuals to determine ARIMA model

I'm having trouble interpreting an ACF/PACF plot of the residuals of a regression to determine what the corresponding ARIMA model would be for the error term. This is the plot of the ACF/PACF of the ...
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1answer
45 views

Forecasting algorithms for incomplete time series data [duplicate]

I want to forecast the demand of each SKU in my warehouse every week from the history transaction that I have collected. The data contains brand, product type, SKU, quantity, date(per day), price. But ...
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ARIMA Model- do i need to include exogenous variables?

How do you tell if exogenous variables should be included or if its ok to just build a model without them (the data speaks for itself).