From 2ec1728c58b4d01e68e67dc19492d9d9a3f03f21 Mon Sep 17 00:00:00 2001
From: MJ Rossetti <s2t2@users.noreply.github.com>
Date: Thu, 31 Oct 2024 17:36:29 -0400
Subject: [PATCH] ACF plot analysis

---
 .../autoregressive-models/autocorrelation.qmd | 58 +++++++++++++++++++
 docs/references.bib                           | 12 ++++
 2 files changed, 70 insertions(+)

diff --git a/docs/notes/predictive-modeling/autoregressive-models/autocorrelation.qmd b/docs/notes/predictive-modeling/autoregressive-models/autocorrelation.qmd
index 40d8580..fdc4ca4 100644
--- a/docs/notes/predictive-modeling/autoregressive-models/autocorrelation.qmd
+++ b/docs/notes/predictive-modeling/autoregressive-models/autocorrelation.qmd
@@ -25,7 +25,65 @@ In addition to interpreting the autocorrelation values themselves, we can examin
   + Slow decay or oscillation often suggests non-stationarity, which may require differencing to stabilize the series.
 
 
+```{python}
+#| code-fold: true
+
+import numpy as np
+import matplotlib.pyplot as plt
+from statsmodels.tsa.arima_process import ArmaProcess
+import statsmodels.api as sm
+
+# Setting random seed for reproducibility
+np.random.seed(42)
+
+# Generating AR(1) process (exponential decay in ACF)
+ar1 = np.array([1, -0.8])  # AR coefficient
+ma1 = np.array([1])        # MA coefficient
+ar1_process = ArmaProcess(ar1, ma1).generate_sample(nsample=100)
+ar1_acf = sm.tsa.acf(ar1_process, nlags=20)
+
+# Generating MA(1) process (significant spike followed by rapid decay)
+ar2 = np.array([1])        # AR coefficient
+ma2 = np.array([1, 0.8])   # MA coefficient
+ma1_process = ArmaProcess(ar2, ma2).generate_sample(nsample=100)
+ma1_acf = sm.tsa.acf(ma1_process, nlags=20)
+
+# Generating non-stationary series with slow decay in ACF
+non_stat_process = np.cumsum(np.random.randn(100))  # Random walk process
+non_stat_acf = sm.tsa.acf(non_stat_process, nlags=20)
+```
 
+```{python}
+#| code-fold: true
+
+import plotly.graph_objects as go
+
+# Creating the ACF plots using Plotly
+
+# Plot for AR(1) process
+fig = go.Figure()
+fig.add_trace(go.Scatter(x=list(range(21)), y=ar1_acf, mode='markers+lines', name='AR(1)'))
+fig.update_layout(title='ACF of AR(1) Process (Exponential Decay)',
+                  xaxis_title='Lag',
+                  yaxis_title='ACF')
+
+# Plot for MA(1) process
+fig.add_trace(go.Scatter(x=list(range(21)), y=ma1_acf, mode='markers+lines', name='MA(1)'))
+fig.update_layout(title='ACF of MA(1) Process (Significant Spike then Rapid Decay)',
+                  xaxis_title='Lag',
+                  yaxis_title='ACF')
+
+# Plot for non-stationary process
+fig.add_trace(go.Scatter(x=list(range(21)), y=non_stat_acf, mode='markers+lines', name='Non-Stationary'))
+fig.update_layout(title='ACF Comparison for AR(1), MA(1), and Non-Stationary Processes',
+                  xaxis_title='Lag',
+                  yaxis_title='ACF',
+                  height=400, # You can set this to any number of pixels you prefer
+                  legend_title='Process Type',
+                  template='plotly_white')
+
+fig.show()
+```
 
 
 
diff --git a/docs/references.bib b/docs/references.bib
index 3bf5340..809bf22 100644
--- a/docs/references.bib
+++ b/docs/references.bib
@@ -59,6 +59,15 @@
 # AUTOCORRELATION
 #
 
+# https://www.investopedia.com/terms/a/autocorrelation.asp
+
+# https://www.ibm.com/topics/autocorrelation
+
+# https://machinelearningmastery.com/gentle-introduction-autocorrelation-partial-autocorrelation/
+
+# Robert Nau
+# https://people.duke.edu/~rnau/411arim.htm
+
 # An Introductory Study on Time Series Modeling and Forecasting
 # Ratnadip Adhikari and R.K. Agrawal.
 # 2013
@@ -88,6 +97,9 @@ @Inbook{Smit1984
     url="https://doi.org/10.1007/978-94-017-1026-8_6"
 }
 
+
+
+
 #
 # ARIMA
 #