S&P 500 INDEX: MODEL SPECIFICATIONS & FORECASTS

Last updated: 06-08-2024
Time: 14:06:53

1. Model Specification

Period:1

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

## OK: residuals appear as normally distributed (p = 0.091).

## OK: Residuals appear to be independent and not autocorrelated (p = 0.898).

## OK: Error variance appears to be homoscedastic (p = 0.223).

## 
##  Bounds F-test (Wald) for no cointegration
## 
## data:  d(SP500) ~ L(SP500, 1) + L(sc, 1) + L(TCI_R, 1) + m1 + indpro +     x_ff + x10_3 + PF + L(cpium, 1) + d(sc) + d(L(sc, 1)) + d(L(sc,     2)) + d(TCI_R) + d(cpium)
## F = 10.821, p-value = 1e-06
## alternative hypothesis: Possible cointegration
## null values:
##    k    T 
##    8 1000

## # Check for Multicollinearity
## 
## Low Correlation
## 
##    Term  VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##  indpro 3.45 [ 2.66,   4.61]         1.86      0.29     [0.22, 0.38]
## 
## Moderate Correlation
## 
##         Term  VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##        TCI_R 5.12 [ 3.87,   6.91]         2.26      0.20     [0.14, 0.26]
##  L(TCI_R, 1) 5.23 [ 3.95,   7.07]         2.29      0.19     [0.14, 0.25]
##        x10_3 9.03 [ 6.70,  12.31]         3.00      0.11     [0.08, 0.15]
## 
## High Correlation
## 
##         Term    VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##  L(SP500, 1)  91.92 [66.74, 126.75]         9.59      0.01     [0.01, 0.01]
##           sc  18.14 [13.30,  24.88]         4.26      0.06     [0.04, 0.08]
##     L(sc, 1)  20.68 [15.14,  28.40]         4.55      0.05     [0.04, 0.07]
##     L(sc, 2)  17.71 [12.98,  24.29]         4.21      0.06     [0.04, 0.08]
##     L(sc, 3)  11.77 [ 8.68,  16.09]         3.43      0.08     [0.06, 0.12]
##           m1  46.85 [34.10,  64.53]         6.84      0.02     [0.02, 0.03]
##         x_ff  18.45 [13.52,  25.32]         4.30      0.05     [0.04, 0.07]
##           PF 120.22 [87.23, 165.82]        10.96  8.32e-03     [0.01, 0.01]
##        cpium  26.30 [19.21,  36.16]         5.13      0.04     [0.03, 0.05]
##  L(cpium, 1)  20.66 [15.12,  28.36]         4.54      0.05     [0.04, 0.07]

## 
##  OLS-based CUSUM test
## 
## data:  ocus
## S0 = 0.64621, p-value = 0.7979

2. Forecasts

## [1] 0.001154174

## [1] 0.001031979

## [1] -2.1237