import numpy as np from statsmodels.tsa.arima.model import ARIMA tseries, b_est = my_MA_gen(0.45, 1000, 50) a1 = [-1.5603521086836527, -0.7331360523813515, -0.6348683454436365, -1.743998275947819, 0.7528849034461478] a2 = [0.45772659] print(np.allclose(a1,tseries[:5])) print(np.allclose(a2,b_est))

True True

***Run error*** Traceback (most recent call last): File "__tester__.python3", line 2, in from statsmodels.tsa.arima.model import ARIMA ModuleNotFoundError: No module named 'statsmodels'

Write a function named my_MA_gen that will generate a time series from the MA(1) modelxt=t+bt1fort=0,1,xt=t+bt1fort=0,1,,wherei={0N(0,1)i<0i0i={0i<0N(0,1)i0.

Within your function, theARIMA class from statsmodelswill then be used to estimate the moving average coefficient bb from the generated time series.

Function call syntax: time_series, b_est = my_MA_gen(b, npts, random_state_val)

• b = MA(1) moving average coefficient
• npts = number of points in the generated time series
• random_state_val = sets the seed for the numpy random number generator
• time_series = Python list containing the generated time series
• b_est = single element numpy vector containing the estimate of the MA coefficient

Example test case:

tseries, b_est = my_MA_gen(0.45, 1000, 50) print(tseries[:5]) print(b_est)

should produce the output

[-1.5603521086836527, -0.8111536578155341, -3.7571214429846274, -1.8369999040892577, -0.5622009685748686] [0.45772998]

You may assume that

import numpy as np from statsmodels.tsa.arima.model import ARIMA

have been invoked.

Answer:(penalty regime: 10, 20, ... %) fix errorsimport numpy as np from statsmodels.tsa.arima.model import ARIMA

def my_MA_gen(b, npts, random_state_val): # Set the random seed for reproducibility np.random.seed(random_state_val) # Initialize the time series list time_series = [] # Generate white noise for the time series eta = np.random.normal(0, 1, npts + 1) # Generate one extra point for eta to accommodate t=0 # Generate the MA(1) time series for t in range(npts): xt = eta[t] + b * eta[t-1] if t > 0 else eta[t] time_series.append(xt) # Convert to numpy array for ARIMA model fitting time_series = np.array(time_series) # Fit the ARIMA model to estimate the MA(1) coefficient model = ARIMA(time_series, order=(0, 0, 1)) fitted_model = model.fit() # Extract the estimated coefficient b_est = np.array([fitted_model.maparams[0]]) return time_series.tolist(), b_est

# Example usage tseries, b_est = my_MA_gen(0.45, 1000, 50) print(tseries[:5]) print(b_est)