Recall the moving average model dt = et − θet−1, where et are independent with mean...

Recall the moving average model dt = et − θet−1, where et are independent with mean 0 and variance σ2. Find its autocorrelation function ρk = Cor(dt,dt−k).

Expert Solution

orchestra answered 3 years ago

Consider the model Yt = ΦYt−3 + et − θet−1, where et has variance σ 2...

Consider the model Yt = ΦYt−3 + et − θet−1, where et has variance σ 2 . (a) Identify Yt as a certain SARIMA(p, d, q) × (P, D, Q)s model. That is, specify each of p, d, q, P, D, Q, and s. You may assume that Φ < 1. (b) Find the variance of Yt . (c) What are the forecasts for Yt+1 and Yt+4? (d) What are the error variances for your forecasts above? (e) If σ...

1. Evaluate the forecasting model using 3 month moving average, and 3 month moving weighted average,...

1. Evaluate the forecasting model using 3 month moving average, and 3 month moving weighted average, and exponential. The weights are .5 for the most recent demand, .25 for the other months. Alpha = .3. Use the weighted moving average for January Forecast. Actual Demand Oct 300 Nov 360 Dec 425 Jan 405 Feb 430 March 505 April 550 May 490 2. Calculate MAD and MAPE for each and compare. Which method is a better forecast and why?

5. The population of certain small organism grows according to the model: dy/dt = 5y where...

5. The population of certain small organism grows according to the model: dy/dt = 5y where y=20 when t=0 t is measured in months. a) Construct the specific function for y. b) Find how many in the population of this organism after 8 months. c) Determine how many months until there are 228 of this organism. Round to the nearest 0.1

What is the mean of an average of independent observations of a random variable? What is...

What is the mean of an average of independent observations of a random variable? What is its standard deviation?

Explain in depth the stationarity conditions for autoregressive (AR) model and moving average (MA) models.

What are the differences between autoregressive and moving average models? Consider the following: model specifications, stationarity,...

What are the differences between autoregressive and moving average models? Consider the following: model specifications, stationarity, the shapes of their autocorrelation and partial autocorrelation functions.

Consider the model as yt= βyt-1 +et, which describes the dynamics of price of a company’s...

Consider the model as yt= βyt-1 +et, which describes the dynamics of price of a company’s stock (y). a. Assuming that et has zero mean, constant variance σe2 and is not serially correlated, obtain expressions for E(yt), var(yt) and cov(yt, yt-1 ) and the first-order auto correlation coefficient. Does y represent a stationary process? Explain briefly. b. If now et follows an AR(1) process, that is et =ρet-1 +vt, where vt is white noise and 0 < ρ < 1,...

Let X1, … , Xn be independent where Xi is normally distributed with unknown mean µ...

Let X1, … , Xn be independent where Xi is normally distributed with unknown mean µ and unknown variance o2 > 0. Find the likelihood ratio test for testing that µ = 0 against −∞ < µ < ∞.

Let X1, … , Xn be independent where Xi is normally distributed with unknown mean µ...

Let X1, … , Xn be independent where Xi is normally distributed with unknown mean µ and unknown variance o2 > 0. Find the likelihood ratio test for testing that µ = 0 against −∞ < µ < ∞.

1) Using a 5 period simple moving average, the forecast for period 13 will be:

Question 1 contains the actual values for 12 periods (listed in order, 1-12). In Excel, create forecasts for periods 6-13 using each of the following methods: 5 period simple moving average; 4 period weighted moving average (0.63, 0.26, 0.08, 0.03); exponential smoothing (alpha = 0.23 and the forecast for period 5 = 53); linear regression with the equation based on all 12 periods; and quadratic regression with the equation based on all 12 periods. Round all numerical answers to two...

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Recall the moving average model dt = et − θet−1, where et are independent with mean...

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Consider the model Yt = ΦYt−3 + et − θet−1, where et has variance σ 2...

1. Evaluate the forecasting model using 3 month moving average, and 3 month moving weighted average,...

5. The population of certain small organism grows according to the model: dy/dt = 5y where...

What is the mean of an average of independent observations of a random variable? What is...

Explain in depth the stationarity conditions for autoregressive (AR) model and moving average (MA) models.

What are the differences between autoregressive and moving average models? Consider the following: model specifications, stationarity,...

Consider the model as yt= βyt-1 +et, which describes the dynamics of price of a company’s...

Let X1, … , Xn be independent where Xi is normally distributed with unknown mean µ...

Let X1, … , Xn be independent where Xi is normally distributed with unknown mean µ...

1) Using a 5 period simple moving average, the forecast for period 13 will be: