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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.

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Do coefficients in moving average process add to 1?

I'm studying weakly stationary stochastic processes, and I'm confused by the title of the "moving average" representation of such a process. Suppose that $y_t$ is a weakly stationary stochastic ...
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Is there a name for a moving average when it is done not across time but some other variable?

The moving average is defined as A method of smoothing a time series to reduce the effects of random variation and reveal any underlying trend or seasonality. (Oxford Dictionary of Statistics, ed. ...
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Arima simulation followed by modeling in R produces bad estimates

Simulate a moving average using arima.sim in R. Then estimate the coefficients using arima. ...
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30 views

Is it possible to calculate the standard deviation of a set that is built from moving averages?

Hope you are all doing fine. I need to calculate the probability of the performance of a X player increasing or decreasing in time. For each ball the X player kicks, he can either score (1) or miss (...
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Forecasting using MA(2) model when past 5 observations are known

So given an MA(2) model : Xt = Wt + Theta1 * Wt-1 + Theta2 * Wt-2 Where Wt is white noise. (Normally distributed) and Theta1 and theta2 were available. Say if X96,X97,...X100 of the series were given ...
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Momentum updates average of g, Adagrad also of g^2 - any other interesting updated averages for SGD convergence?

Updating exponential moving average is a basic tool of SGD methods, starting with of gradient $g$ in momentum method to extract local linear trend from the statistics. Then e.g. Adagrad, ADAM family ...
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Are there limitations to backshift operator algebra in Time Series Analysis?

After algebraic gymnastics with the backshift operator $\text{B}$ (i.e., $\text{B}y_t=y_{t - 1}$) I thought I found a convenient dynamic representation for a nonlinear model, but the representation ...
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Why doesn't the Wold's decomposition theorem imply a good AR(p) fit?

I'm trying to fit an AR(p) process to the standardized, 10 years long time series of monthly logreturns of a stock index and get extremely poor fit. I'm not surprised, because if I had a good fit, ...
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R - Moving average; MA(2), Maximum-Likelihood estimation through optim routine

I am trying to complete my assignment for time-series where I have to use Nile data to fit MA(2) model and estimate theta coefficients through creation of new function and optimizing it to get ...
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37 views

ARIMA MODEL DEGREE OF FREEDOM PROOF

According to arima(p,0,q) model if we have n data and our total parameter is p+q then it is said that degree of freedom is n-(p+q). Could you mathematically demonstrate it? No sufficient information ...
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58 views

Is it good practice to use Linear Least-Squares with SMA?

I have time-series (daily) data and I want to understand the general trend. My current approach is: Calculate the 7-day simple moving average. Add a line of best fit (linear least squares ...
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Moving average process - stationarity

If we consider a moving average process of order 1, is that stationary? Because, although, the mean will remain the same for Yt and Yt+k, the variance and co-variance will change if you calculate ...
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36 views

Moving Average Method

Suppose I have data for 6 months: $2,5,1,9,3,4$. If I calculate 3 months moving average, then from this data, I get two average $2.667(=\frac{2+5+1}{3})$ and $5.333(=\frac{9+3+4}{3})$. But if I have ...
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What is the best calculation method to account for individual change, volatility, observation windows and time decays in time series data? ARIMA, ETS?

I am looking at applying a theoretical best calculation method to some particular time series (ts) data. Ideally the calculation method would encompass relative change in individual ts, volatility of ...
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Confusing terminology of TimeSeries: “Smoothing” and “Differencing” [closed]

I studied MA, AR, ARIMA, SARIMA to forecast products demand using python, but recently I encountered the smoothing, using ...
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1answer
20 views

importance sampling and exponential moving average

Lets say i have got a random variable $X$ with samples $x_t\sim X$ and density $p_X(x)$ and want to compute its mean via a moving average $ \mu_{t+1}=(1-c)\mu_t + c x_t$ Assume, I can not observe $X$...
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Moving Average Representation of a Stationary Time Series

I was wondering if this equation is considered a Moving Average process of order 13? If so, does that mean that the coefficients at times t-2 to t-11 are 0? As they are clearly not present in this ...
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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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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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Prediction interval for rolling average forecast

In agile software development average of last 3 delivered periods (sprints) is taken to forecast next periods deliverables. I'm not here to discuss if the approach is correct or not. ;) According to ...
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55 views

How to deal with expected value in the context of time series?

For example, in this MA(2) model, $y_t = u_t + \phi u_{t-2}$ $u_t$ is identically, independently, normally distributed with a mean of 0 and a variance of $\sigma^2$. (Does variance matter here?) I ...
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114 views

Where does the white noise come from in MA(q) model?

I'm having trouble understanding the intuition of the moving average model. How does summing up a bunch of white noises related to predicting your particular time series data? Suppose I have a MA(q) ...
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36 views

Is there a function that combines correlation and convolution?

I'm actually trying to find some correlations between functions, and i was wondering if there is a function that quantifies the amount of time we need to shift a curve to have a high correlation with ...
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41 views

Confused with textual explanation of moving average

I have two questions about moving average calculation in Python vs moving average example in a textbook. The task is to calculate a three-year moving average. In Python, I am using df['...
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Thomas Sargent's intuition as to why every covariance stationary series has an infinite-order Wold representation

In his classic book "Time Series Analysis", James Hamilton references Thomas Sargent (["Dynamic Macroeconomic Theory"], 1987, pp. 286-290) as a "nice sketch of the intuition behind this result [Wold ...
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What guarantees the existence of a finite representation of the Wold decomposition? Mechanics and Intuition

Every covariance stationary process can be written as a linear, infinite distributed lag of white noise. In other words, every covariance stationary process has a Wold representation. Then we go on to ...
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Is there a filter function that performs similar to moving average but does not loose data?

I need to smooth a time series using a low pass filter. A simple moving average is working fine for me, however, using a moving average causes an inevitable loss of data a the beginning of the ...
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143 views

Memoryless Property of a Markov Chain of Order 1. Is AR(1) memoryless or of infinite memory?

A stochastic process constitutes a discrete Markov Chain of order 1 if it has the memoryless property, in the sense that the probability that the chain will be in a particular state i, of a finite set ...
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47 views

General Form of Arima(2,1,2)

There is a question in my textbook that asks for the ARIMA(2,1,2) model. I get how to do the AR and the MA parts, but I'm having a little trouble understanding the differencing portion of the model. ...
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156 views

How to relate roots of AR and MA to unit circle

I'm working on these problems and think I figured out most of the steps, but am stuck near the end as I don't understand how to relate my roots back to the unit circle in order to determine ...
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Showing the 2nd Order Properties of 2 ARMA Processes are Identical

Given 2 processes $$ Z_t = \epsilon_t + \theta\epsilon_{t-1} $$ $$ Z_t' = \epsilon_t' + \theta^{-1}\epsilon_{t-1}' $$ where $$ \epsilon_t \overset{iid}{\sim}\mathcal{N}(0, \sigma^2) $$ $$ \epsilon_t' ...
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Calculated Projected “End Date” for Event

In reviewing average event duration (such as a service call), I notice that the most recent event average duration appears to be falling; appears to be a trend in event time reduction. However, only ...
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52 views

How do I identify the magnitude of the difference between two moving averages?

I am trying to identify not only when two moving averages diverge, but when they do so by enough for it to be important. With the data I am using (not stock market data), the two averages will cross ...
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60 views

What is the meaning of having the autocorelation function a cut of at a specific lag and at the same time the partial autocorrelation tails off

having the case that the ACF have only, for example on spike at lag 1 , and the PACF decays exponentially this is a MA model signature. but what is the meaning of having the a value at a the lag K on ...
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Understanding a derivation of bias correction for the Adam optimizer

I'm reading paper about the Adam optimizer and went up until the bias-correction section; in the paper they estimate the bias of the moving average of the squared gradient. These are the equations ...
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Smallest effective window for EWMA

I'm using an EWMA class to calculate an exponentially weighted moving average. What I'm measuring is the rate at which bytes are arriving at my server for each client that sends a request. I want to ...
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1answer
204 views

What is a correct implementation of the moving average model

I would like to implement a moving average model in python as when I try to use the statsmodels library, specifically the ARMA(p,q) function and setting $p=0$ I get a lot of convergence errors in the ...
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50 views

what does the constant term in the Moving average model represents?

that equation is gotten from here. Is that mean term represents the best fit for the bias term for MA model gotten by minimizing the mean squared error equation?
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43 views

How the error is generated in MA process?

If a time series process depends on its own past values then it's a AR process. These is what i understood but if it depends on it's own error then it's a MA process. Here is where i get confused. ...
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113 views

Best Predictor of MA(1)

I have read a statement in a lecture note that for an MA(1) model $X_t = \theta \epsilon_{t-1} + \epsilon_t$ with $|\theta| < 1$, where $\epsilon_t$ are white noise variates: We can forecast only ...
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Enforce invertiblity of an MA(q) process with non-unit coefficient

Consider the MA(p) process $ y_t = \theta_0 \varepsilon_t + \theta_1 \varepsilon_{t-1} + \ldots + + \theta_q \varepsilon_{t-q} $, where $\theta_0 \neq 1$, contrary to the convention taken in most ...
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Writing AR(1) as a MA($\infty$) process

The AR(1) process is $$ X_t = \phi X_{t-1} + \varepsilon_t $$ if we use this formula recursively, we get $$ X_t = \phi(\phi X_{t-2} + \varepsilon_{t-1}) + \varepsilon_t = \phi^2X_{t-2} + \phi\...
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49 views

How to determine optimal “threshold” for taking in averages of data?

Sorry in advance if this isn't the right place for this question. I'm working on a project to try to determine whether a particular object is is producing sound or not. I'm using a piece of hardware ...
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52 views

Invertibility conditions for MA models

Many textbooks and notes use geometric series to build a relationship between the inverse of the lag operator and that of a polynomial function as below. Inverse of the lag operator $\phi^{-1}(L) = ...
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73 views

Is there a simple way to explain the parameter estimation process of MA or ARMA?

I know the ordinary least squares and gradient decent methods that are used to estimate the parameters (weights) in linear regression. But I am not that good at math and I can't understand the ...
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AR($1$) - autocovariance

I used the autocovariance formula that was in my textbook for the MA($1$) and applied it to the AR($1$) model but did not get the right answer. Can someone please explain to me why the below ...
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Conceptual questions on efficient estimators for MA model

I am trying to estimate parameters of a MA(p) system where p is the order. E.g., $$y[n] = \sum_{i=1}^p {\theta}_i u[n-i] + e[n] = \mathbf{\theta}^T\mathbf{u}[n] + ...
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51 views

ARIMA doesn't include the trend

I have a problem with my ARIMA(1,1,1) predictions. I have a time series with no seasonal component but with an obvious trend. To get rid of it I take the first difference by setting d=1. The model ...
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67 views

Cumulative Moving Trimmed Mean [closed]

I would be interested in a technique to calculate the trimmed mean of a (potentially) infinite stream of observations. It is infeasible to store each of the observations and therefore, I have to ...
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42 views

Evaluating the quality of a moving average

I have a statistics scenario that doesn't contain a huge number of samples and am trying to set some inputs in the most appropriate way. The data can basically be thought of as having a date, a ...