S&P 500 INDEX: MODEL SPECIFICATIONS & FORECASTS

Last updated: 06-08-2024
Time: 14:08:27

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 = 0.281).

## OK: Residuals appear to be independent and not autocorrelated (p = 0.598).

## OK: Error variance appears to be homoscedastic (p = 0.095).

## 
##  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(L(SP500, 1)) + d(sc) +     d(L(sc, 1)) + d(TCI_R) + d(cpium)
## F = 10.46, 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 3.44 [ 2.66,   4.60]         1.86      0.29     [0.22, 0.38]
## 
## Moderate Correlation
## 
##         Term  VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##        TCI_R 5.16 [ 3.91,   6.96]         2.27      0.19     [0.14, 0.26]
##  L(TCI_R, 1) 5.19 [ 3.92,   6.99]         2.28      0.19     [0.14, 0.25]
##        x10_3 8.15 [ 6.08,  11.08]         2.86      0.12     [0.09, 0.16]
## 
## High Correlation
## 
##         Term    VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##  L(SP500, 1) 128.53 [93.43, 176.97]        11.34  7.78e-03     [0.01, 0.01]
##  L(SP500, 2)  85.06 [61.89, 117.07]         9.22      0.01     [0.01, 0.02]
##           sc  17.77 [13.05,  24.33]         4.22      0.06     [0.04, 0.08]
##     L(sc, 1)  22.55 [16.52,  30.92]         4.75      0.04     [0.03, 0.06]
##     L(sc, 2)  11.66 [ 8.62,  15.91]         3.41      0.09     [0.06, 0.12]
##           m1  42.32 [30.87,  58.16]         6.51      0.02     [0.02, 0.03]
##         x_ff  16.20 [11.92,  22.17]         4.03      0.06     [0.05, 0.08]
##           PF 114.32 [83.12, 157.38]        10.69  8.75e-03     [0.01, 0.01]
##        cpium  22.69 [16.62,  31.11]         4.76      0.04     [0.03, 0.06]
##  L(cpium, 1)  21.14 [15.50,  28.98]         4.60      0.05     [0.03, 0.06]

## 
##  OLS-based CUSUM test
## 
## data:  ocus
## S0 = 0.65976, p-value = 0.7767

2. Forecasts

## [1] 0.001178513

## [1] 0.001038535

## [1] 4.811957