S&P 500 INDEX: MODEL SPECIFICATIONS & FORECASTS

Last updated: 06-08-2024
Time: 15:50:33

1. Model Specification

Period:55

Specification:
SP500=f(SC, TCI_R, m1, indpro, x_ff, x10_3, PF, cpium)

## OK: residuals appear as normally distributed (p = 0.583).

## OK: Residuals appear to be independent and not autocorrelated (p = 0.514).

## OK: Error variance appears to be homoscedastic (p = 0.718).

## 
##  Bounds F-test (Wald) for no cointegration
## 
## data:  d(SP500) ~ L(SP500, 1) + sc + L(TCI_R, 1) + m1 + L(indpro, 1) +     L(x_ff, 1) + L(x10_3, 1) + PF + cpium + d(TCI_R) + d(indpro) +     d(x_ff) + d(x10_3)
## F = 5.4906, p-value = 0.0003607
## alternative hypothesis: Possible cointegration
## null values:
##    k    T 
##    8 1000

## # Check for Multicollinearity
## 
## Moderate Correlation
## 
##          Term  VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##         TCI_R 6.30 [ 4.58,   8.86]         2.51      0.16     [0.11, 0.22]
##   L(TCI_R, 1) 7.65 [ 5.52,  10.79]         2.77      0.13     [0.09, 0.18]
##        indpro 9.56 [ 6.85,  13.52]         3.09      0.10     [0.07, 0.15]
##  L(indpro, 1) 8.37 [ 6.02,  11.81]         2.89      0.12     [0.08, 0.17]
##         cpium 9.43 [ 6.76,  13.33]         3.07      0.11     [0.08, 0.15]
## 
## High Correlation
## 
##         Term    VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##  L(SP500, 1)  65.69 [46.03,  93.93]         8.11      0.02     [0.01, 0.02]
##           sc  15.94 [11.30,  22.66]         3.99      0.06     [0.04, 0.09]
##           m1  47.20 [33.13,  67.45]         6.87      0.02     [0.01, 0.03]
##         x_ff  94.21 [65.94, 134.78]         9.71      0.01     [0.01, 0.02]
##   L(x_ff, 1) 130.22 [91.08, 186.37]        11.41  7.68e-03     [0.01, 0.01]
##        x10_3  28.99 [20.41,  41.35]         5.38      0.03     [0.02, 0.05]
##  L(x10_3, 1)  30.97 [21.79,  44.19]         5.56      0.03     [0.02, 0.05]
##           PF  91.09 [63.76, 130.31]         9.54      0.01     [0.01, 0.02]

## 
##  OLS-based CUSUM test
## 
## data:  ocus
## S0 = 0.42367, p-value = 0.9939

2. Forecasts

## [1] 0.001268746

## [1] 0.001042357

## [1] 2.668342