S&P 500 INDEX: MODEL SPECIFICATIONS & FORECASTS

Last updated: 06-08-2024
Time: 15:49:21

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 = 0.597).

## OK: Residuals appear to be independent and not autocorrelated (p = 0.452).

## OK: Error variance appears to be homoscedastic (p = 0.748).

## 
##  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 = 5.5388, p-value = 0.0003298
## 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 6.27 [ 4.55,   8.82]         2.50      0.16     [0.11, 0.22]
##   L(TCI_R, 1) 7.76 [ 5.59,  10.95]         2.79      0.13     [0.09, 0.18]
##        indpro 9.54 [ 6.83,  13.50]         3.09      0.10     [0.07, 0.15]
##  L(indpro, 1) 8.37 [ 6.02,  11.83]         2.89      0.12     [0.08, 0.17]
## 
## High Correlation
## 
##         Term    VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##  L(SP500, 1)  65.70 [45.99,  94.04]         8.11      0.02     [0.01, 0.02]
##           sc  17.06 [12.07,  24.29]         4.13      0.06     [0.04, 0.08]
##           m1  48.37 [33.90,  69.18]         6.95      0.02     [0.01, 0.03]
##         x_ff  92.63 [64.77, 132.66]         9.62      0.01     [0.01, 0.02]
##   L(x_ff, 1) 128.97 [90.11, 184.77]        11.36  7.75e-03     [0.01, 0.01]
##        x10_3  28.56 [20.09,  40.78]         5.34      0.04     [0.02, 0.05]
##  L(x10_3, 1)  31.86 [22.39,  45.51]         5.64      0.03     [0.02, 0.04]
##           PF  88.26 [61.72, 126.40]         9.39      0.01     [0.01, 0.02]
##        cpium  10.24 [ 7.32,  14.52]         3.20      0.10     [0.07, 0.14]

## 
##  OLS-based CUSUM test
## 
## data:  ocus
## S0 = 0.43925, p-value = 0.9905

2. Forecasts

## [1] 0.0012193

## [1] 0.0009878648

## [1] 4.033902