Skip to main content

Questions tagged [moving-average]

In time series analysis, the moving-average (MA) model is a common approach for modeling univariate time series. The moving-average model specifies that the output variable depends linearly on the current and various past values of a stochastic (imperfectly predictable) term.

Filter by
Sorted by
Tagged with
0 votes
0 answers
8 views

Suggested techniques to model forward moving averages

I want to start a personal project, but i'm failing to formulate my business problem into a model. I would love inputs on how to better look into this issue and what type of models/techniques i should ...
Brites's user avatar
  • 1
0 votes
1 answer
19 views

how to summarize moving average

This question is about how to summarize moving averages. Please assume the values in column Pct are % of people how have negative opinion about vaccine. column MovgAvg is the two year moving average ...
Ahir Bhairav Orai's user avatar
0 votes
0 answers
13 views

Mean of weekly data smoothed with a 3-week moving average

I have weekly Influenza data for 6 years and I want to find the mean to plot over time so that I can compare to the weekly data for 2024 so far (here is the dataset). The problem I have is that the ...
R Maharaj's user avatar
  • 191
1 vote
0 answers
35 views

Forecasting ARIMA(0,0,1) model by hand - trouble with MA elements

I am having issues forecasting a stationary ARIMA(0,0,1) time-series. I currently have 500 observations of the process, and want to predict the coming three periods. Using Stata software, I am able to ...
Ohoma's user avatar
  • 11
3 votes
1 answer
46 views

How to determine (the lag order of) MA from these plots?

I am using time series to analyze the price of a commodity. Characterizing is the fact that the price of the good is determined per hour, one day prior to the day of delivery. For now, I have ...
Zillah's user avatar
  • 31
0 votes
0 answers
14 views

Autoregressive Process to Moving Average Representation

Suppose that we have an autoregressive process with order 1: $$y_t = a + {\alpha}y_{t-1}+u_t$$ for $t>k$, where $k$ is a positive integer and $\alpha \in (0,1)$. And, $$y_t = b + {\alpha}y_{t-1}+...
user722271's user avatar
0 votes
0 answers
6 views

Difference transformation and Stationarization of Moving Average

I have a temperature sensor data, I want to denoise it. The first thing that came to my mind was to take the moving average, it was very smooth but it is still not stationary. If I take the log ...
Clankk's user avatar
  • 33
0 votes
0 answers
12 views

How to calculate the process control limits when there is not much data left?

Context: To compute the "Process Control" limits, I am following the Stacey Barr's blog. My question: After detecting the signal, if I don't have enough data points left in my dataframe, for ...
Deepak Tatyaji Ahire's user avatar
1 vote
0 answers
72 views

VMA to VECM representation

I'm doing research at the moment and for estimation purposes I need to convert a VMA (equation 9.2.2 in the attached picture) to a VECM model (9.2.1) in picture; does anyone know how to make this ...
user406838's user avatar
2 votes
1 answer
55 views

Is it legit to compute/define moving average series for a stationary process?

Suppose we have $X_{1}, X_{2}, ..., X_{n}$ sequence of $iid$ random variables with mean $\mu$ and standard deviation $\sigma$. By definition, the time series $x_{1}, x_{2}, ..., x_{n}$ is a stationary ...
Sane's user avatar
  • 489
2 votes
2 answers
79 views

Why is a Moving Average Process not just noise? [closed]

I was studying Moving Average Processes, and wanted to ask why adding a bunch of weighted noise terms is not just a noise term. I understand the operations involving mean and variance in a ...
insipidintegrator's user avatar
2 votes
1 answer
124 views

More about the deterministic part of Wold decomposition

This is a follow-up on this question of mine. Wold's representation theorem states that every covariance-stationary time series $\{Y_t\}$ can be written as the sum of two time series, one ...
Richard Hardy's user avatar
1 vote
0 answers
35 views

Is my motivation for ARMA accurate?

I think I finally understand the point of the 'moving average' part of ARMA/ARIMA, but I wanted to confirm here, just in case I am still off. Idea 1: Autoregressive processes are easy to motivate - ...
Terence C's user avatar
  • 172
1 vote
1 answer
63 views

Smoothing out target variable for spiky demand forecasting

I am trying to predict ambulance demand for the next hour, for a city area in the USA, based on previous demand, weather, large people gatherings, and similar spatio-temporal factors - using Machine ...
Nadir Bašić's user avatar
0 votes
0 answers
25 views

Convergence of Truncated and Subsequenced MA($\infty$) Processes with Square Summable Coefficients

Let $X_t=\sum_{j=0}^{\infty} \phi_j \varepsilon_{t-j}$ be an MA($\infty$) process with square summable coefficients. We know that if we truncate the process at $n$, creating the sequence: $$X_{t,n} = \...
user346624's user avatar
0 votes
1 answer
29 views

Does moving average smoothing affect future forecasts of a time series?

I'm trying to make a multivariate time series forecast using endogenous variables. My features show a lot of spikes (noise), and as I was researching some steps to handle it, I found moving average ...
Patrick Priyadharshan's user avatar
2 votes
0 answers
25 views

Why can MA(q) (Moving Average Model with lag q) not predict q timesteps in the future [closed]

I understand that the equation for Moving Average model for lag q is - $$ y_t = \mu + \epsilon_t + \theta_1\epsilon_{t-1}+ \theta_2\epsilon_{t-2}+\dots+ \theta_q\epsilon_{t-q} $$ lets say we have ...
Ashwathama's user avatar
0 votes
0 answers
30 views

Applying filter (e.g., moving average) on Binomial distributed random values

I start with Binomial distributed random values with known $N$ and success probability $p$. I can easily estimate PMF and CDF of such distribution. Now assume these Binomial distributed random values ...
user avatar
2 votes
0 answers
63 views

Solving an exercise about admissible coefficient values for a MA(1) process

I'm studying "Principles of system identification : Theory and Pratice" by Arun K. Tangirala and well... I've just entered the part about moving averages and I'm confused. I don't understand ...
NokiYola's user avatar
  • 121
2 votes
1 answer
116 views

How come the deterministic part of Wold decomposition does not violate stationarity?

Wold's representation theorem states that every covariance-stationary time series $\{Y_t\}$ can be written as the sum of two time series, one deterministic and one stochastic: $$ Y_t=\sum_{j=0}^\infty ...
Richard Hardy's user avatar
0 votes
0 answers
41 views

auto.arima (Hyndman R package)

I am running an auto arima on a datase that yields two tries as revealed by using trace=TRUE as: ...
Emil Partsch's user avatar
0 votes
0 answers
32 views

ARIMA(0,0,3) fitted values and residuals in R

I am trying to understand the residuals returned from a fitted ARIMA(0,0,3) model. I simulated a time series and recovered the parameters: ...
user42927's user avatar
3 votes
1 answer
258 views

Maximum value of ACF at lag 1 for $\text{MA}(q)$ process

Given an $\text{MA}(1)$ process with parameter $\theta_1$, we know that $$ \rho(1) = \frac{\theta_1}{1+\theta_1^2} $$ which has a maximum value of 0.5 when $\theta_1 = 1$. I saw somewhere (I don't ...
Jesús A. Piñera's user avatar
2 votes
0 answers
81 views

How can I find the unconditional variance of this process?

Let $y_t = \Delta p_t$ denote a time series of asset returns, where $p_t$ are logarithmic prices. $y_t$ is generated by a heteroskedastic MA(1) process \begin{aligned} y_t &= z_t+\theta z_{t-1}, \\...
V013's user avatar
  • 115
1 vote
1 answer
44 views

ARIMA flattens out on one order and works perfect on another

I am implementing an ARIMA model on a time series data. I have confirmed that the data is stationary with the adfuller test. I plotted my ACF and PACF graph as below with a lag of 40. Here, I see the ...
Omkar Kulkarni's user avatar
0 votes
0 answers
24 views

Interpretation of Moving Average coefficient in ARIMA and its equivalance with exponential smoothing parameter

On Running an ARIMA (0,0,1) model from statsmodels.api on a differenced time series say X(t). I get the following output const = 5.34e-06 ma.L1 = 0.8934 How should I interpret the above MA model with ...
Math lover's user avatar
0 votes
0 answers
27 views

How to test a MA process with extra terms for invertibility?

I'm working on an unassessed course problem (paraphrased for brevity), Consider the time series model $$y_t=\alpha+\beta t+\epsilon_t$$ where $\epsilon_t$ is a white noise and $\alpha,\beta$ are ...
mjc's user avatar
  • 599
0 votes
1 answer
373 views

Estimating the decay parameter in Exponentially Weighted Moving Average (EWMA) model

Given the data $y_t$, $t=1, \cdots ,N$; I would like to estimate the decay parameter $\lambda$ in Exponentially Weighted Moving Average (EWMA) model, such that $y_{t+1} = \sum_{k=0}^K \lambda^k y_{t - ...
Stephen Ge's user avatar
0 votes
0 answers
14 views

Improving an ARIMA model by eliminating AR/ME terms

I've come over the following two statements to manually improve the fit of an ARIMA model by changing its parameters $p,q$. If the AR coefficients sum to nearly 1 and suggest a unit root in the AR ...
Daraan's user avatar
  • 103
0 votes
0 answers
28 views

How to apply moving average with multiple identical dates

I have dataset with a (unique) ID, a date (yyyy-mm-dd format) and an arbitrary measuring value x. The dataset is sorted by date (first) and, multiple IDs have the same date, by ID (second). If I plot ...
Lukas's user avatar
  • 111
0 votes
0 answers
22 views

An MA model has MA characteristic polynomial $(1 − 1.4x + 0.3x^2 )(1 + 0.5x^{12})$, obtain the model [duplicate]

When the characteristic polynomial of a moving average s model is given as $(1 − 1.4x + 0.3x^2 )(1 + 0.5x^{12})$, how to obtain the MA model and then calculate the ACF of this model? I am expecting ...
Kavindu Ravishka's user avatar
3 votes
0 answers
20 views

Missing assumption in MA estimation

Assume we observe a $MA(1)$ process for which it is known that the mean is zero. Based on a series of length $3$ , we observe $Y_1 = 0, Y_2 = 1$ and $Y_3 = 0.5$. Find the least-squares estimate of $\...
Kilkik's user avatar
  • 445
0 votes
0 answers
62 views

Prediction error variance MA(1) process

I was looking at the prediction error variance of an MA(1) process and we saw the following derivation for the prediction error variance. I understand the first part of this derivation but I am ...
Marie's user avatar
  • 3
1 vote
2 answers
69 views

$\theta_0=1$ in MA process

Let $X_t$ be an MA$(q)$ process defined as \begin{equation} X_{t}=\mu +\overset{q}{\underset{j=0}{\sum }}\theta_{j}\varepsilon_{t-j}=\mu +\theta_{0}\varepsilon_{t}+\theta_{1}\varepsilon_{t-1}+\theta_{...
Kilkik's user avatar
  • 445
2 votes
0 answers
16 views

$A^{-1}$ in the Triangular factorisation of a MA(1) process [closed]

I am trying to confirm the what the $A^{-1}$ actually is in a triangular factorisation of the variance-covariance of a MA(1) process. And what I have found doesn't seem to match what is on Hamilton p....
blackvegetable's user avatar
3 votes
1 answer
59 views

If $X_t$ is an AR(2) process, what is $Y_t := X_t - X_{t-1}$?

Q: If $X_t$ is an AR(2) process, what is $Y_t := X_t - X_{t-1}$? Attempted solution: $X_t = \phi_1 X_{t-1} + \phi_2 X_{t-2} + W_t$, where $W_t$ is white noise. \begin{equation} \begin{split} Y_t &:...
Oskar's user avatar
  • 265
1 vote
0 answers
38 views

Is there a statistically sound method of smoothing a data series without removing the edges?

Recently I've been plotting a lot of data, and often I find myself using a moving average to smooth out values that oscillate or otherwise fluctuate a lot. However, the problem with this is that it ...
Outis Nemo's user avatar
0 votes
0 answers
66 views

Exponential Averaging using Simple averaging

Mathematically what is the expression that is close to a 10 Day Exponential moving average (span of 10 means decay factor of 0.818181) that is created using averaging over Simple moving averages. E.g. ...
Dhruv Mahajan's user avatar
2 votes
0 answers
375 views

VARMAX model in r | Fit VARMA model including exogenous variable [closed]

Working on VARX model and I want to include MA term here but I have not found any package in R to build VARMAX model. MTS package can be used to fit VARMA model but I want to include exogenous ...
Aditya Malani's user avatar
1 vote
1 answer
43 views

How to write it as the linear process for MA(2) when the characteristic root is complex? [closed]

I have MA(2) as $$x_t=e_t-0.3e_{t-1}+0.1e_{t-2}$$ and would like to find $x_{t+1}$. But I struggle and $$x_t(1-0.3B+0.1B^2)^{-1}=e_t.$$ I can't write it as linear process because the root of the ...
Pandora's user avatar
  • 11
0 votes
0 answers
42 views

Does $ARMA(p,q)$ process need to be invertible and have a causal stationary solution to be written in $MA(\infty)$ representation?

Does $ARMA(p,q)$ process need to be invertible and have a causal stationary solution to be written in $MA(\infty)$ representation? And if you write the process in terms of $Z_t$ instead of $X_t$, then ...
eddie's user avatar
  • 207
2 votes
1 answer
103 views

are moving average and lag modeling the same?

I am not clear on the difference between the two concepts but I am interested in air pollution exposure in a given period of time and in the literature, I know that lag models are used. I have also ...
ineedhelp's user avatar
  • 355
0 votes
0 answers
62 views

Covariance function of MA(1) process

probably answered before but I would I want to see if my reasoning is correct, as my textbook skips the calculations but the answer coincide. Q: Let $Z_t \sim \text{WN}(0, \sigma^2)$ (white noise), ...
Oskar's user avatar
  • 265
3 votes
2 answers
232 views

Show process is $ARMA(1,1)$

Consider this exercise taken from Brockwell and Davis (1991): I'm a bit confused as to how that implies $Y_t$ is $ARMA(1,1)$. I've tried to show it, but I end up going back in circles, and I'm not ...
eddie's user avatar
  • 207
2 votes
1 answer
113 views

$MA(q)$ : Show $\sqrt{n}\hat{\rho}(q + l)\overset{d}{\to} N(0, 1 + 2\sum _{j=1}^q\rho ^2\left(j\right)), l\ge 1 $

I am trying to show that for an $MA(q)$ process, $$\sqrt{n}\hat{\rho}(q + l)\overset{d}{\to} N(0, 1 + 2\sum _{j=1}^q\rho ^2\left(j\right)), \quad l\ge 1. $$ I'm having a hard time doing this. I'm not ...
eddie's user avatar
  • 207
1 vote
0 answers
31 views

A question about an estimation using moving average and moving standard deviation?

Given a time series data $\{X_t\}_{t = 0}^\infty$, what does its moving average and moving standard deviation estimate when there is no assumption that $\mathbb{E}[X_t] = \text{const}, \forall t$? ...
Zhang Qifan's user avatar
1 vote
1 answer
176 views

Prove that a random variable follows MA(1) process

I have the follow variable $$y_t = e_t + u_t + \theta u_{t-1}$$ Here $u_t$ and $e_t$ are mutually independent i.i.d and $u_t \sim N(0, \sigma_u^2)$ and $e_t \sim N(0, \sigma_e^2)$. I am trying to show ...
Lola1993's user avatar
0 votes
1 answer
54 views

Why do we use moving averages in evaluation process for Batch Normalization layer?

I have seen many links about MA for batch normalization but nothing answered my question. In Batch normalization, you get means and variance for each mini-batches in the training process. And the ...
abj's user avatar
  • 1
1 vote
1 answer
58 views

Online Estimation of a Joint Distribution from batches of data

I want to implement an algorithm for the online estimation of a joint probability distribution from a sequence of mini batches sampled from the real distribution. The distribution is discrete and non ...
Bach05's user avatar
  • 11
0 votes
1 answer
315 views

exponential moving average taking into account different time intervals

i want to calculate the exponential moving average with the following formula EMAt = valt * α + EMAt - 1 * (1 - α) but i don't have all the data, i only have some data with a big gap in time. while ...
ashura's user avatar
  • 1

1
2 3 4 5
8