#!/usr/bin/env python
# coding: utf-8

# # Monte Carlo Simulation of Time Series
# 
# **Randall Romero Aguilar, PhD**
# 
# This demo is based on the original Matlab demo accompanying the  <a href="https://mitpress.mit.edu/books/applied-computational-economics-and-finance">Computational Economics and Finance</a> 2001 textbook by Mario Miranda and Paul Fackler.
# 
# Original (Matlab) CompEcon file: **demqua10.m**
# 
# Running this file requires the Python version of CompEcon. This can be installed with pip by running
# 
#     !pip install compecon --upgrade
# 
# <i>Last updated: 2022-Oct-23</i>
# <hr>
# 

# ## About
# Simulate time series using Monte Carlo Method.
# 
# A commodity price is governed by weekly price movements
# \begin{equation*}
# \log(p_{t+1}) = \log(p_t) + \tilde \epsilon_t
# \end{equation*}
# where the $\tilde \epsilon_t$ are i.i.d. normal with mean $\mu=0.005$ and standard deviation $\sigma=0.02$.
# 
# To simulate three time series of T=40 weekly price changes, starting from a price of 2, execute the script

# ## Initial tasks

# In[1]:


import numpy as np
from scipy.stats import norm
import matplotlib.pyplot as plt
plt.style.use('seaborn')


# ## Simulation

# In[2]:


m, T = 3, 40
mu, sigma = 0.005, 0.02
e = norm.rvs(mu,sigma,size=[T,m])
logp = np.zeros([T+1,m])
logp[0] = np.log(2)
for t in range(T):
    logp[t+1] = logp[t] + e[t]


# ## Make figure

# In[3]:


fig, ax = plt.subplots()
ax.set(xlabel='Week', ylabel='Price', xlim=[0,T])
ax.plot(np.exp(logp));