User specific mean and variance for alpha and beta in Regression

[sourish-cmi]

User-specific mean and variance for alpha and beta in Regression

[sourish-cmi]

Design requirement

fit( formula::FormulaTerm, data::DataFrame,modelClass::LinearRegression
,prior::Prior_Ridge,alpha_prior_mean::Float64 = 0.0, beta_prior_mean::Float64
,alpha_prior_sd::Float64,beta_prior_sd::Vector{Float64}
,sim_size::Int64 = 1000,h::Float64 = 0.01)

[sourish-cmi]

Example

fit(rt_tcs ~ rt_nifty, data_frame, LinearRegression(), Prior_Gauss(), alpha_prior_mean  = 0.0, beta_prior_mean = 1.0,alpha_prior_sd=0.2, beta_prior_sd=0.6, sim_size=5000)

@ajaynshah please confirm - if that what you want?

[sourish-cmi]

Here is the implementation:

using Dates
using MarketData
using Impute
using DataFrames
using TSx
using CRRao
using StatsModels

startdate = DateTime(2012, 10, 1)
options = YahooOpt(period1 = startdate)

infy = MarketData.yahoo("INFY.NS", options) |> DataFrame
nifty = MarketData.yahoo("^NSEI", options) |> DataFrame

# Closing prices with filled in missing values
infy_close = TS(infy[:, [:timestamp, :AdjClose]])
nifty_close = TS(nifty[:, [:timestamp, :AdjClose]])

data = join(infy_close, nifty_close, JoinBoth)
TSx.rename!(data, [:infy, :nifty])

data = TS(data.coredata |> Impute.locf())

weekly = data[endpoints(data, Week(1))]
weekly_returns = diff(log(weekly))
# weekly_matrix = Matrix(weekly_returns)
df = dropmissing(weekly_returns.coredata)

classical = fit(@formula(infy_log ~ nifty_log), df, LinearRegression())

julia> classical = fit(@formula(infy_log ~ nifty_log), df, LinearRegression())
Model Class: Linear Regression
Likelihood Mode: Gauss
Link Function: Identity
Computing Method: Optimization
──────────────────────────────────────────────────────────────────────────────
                  Coef.  Std. Error      t  Pr(>|t|)     Lower 95%   Upper 95%
──────────────────────────────────────────────────────────────────────────────
(Intercept)  0.00201197  0.00144211   1.40    0.1636  -0.000821097  0.00484505
nifty_log    0.661467    0.0630299   10.49    <1e-22   0.537643     0.78529
──────────────────────────────────────────────────────────────────────────────

## Bayesian prior
## alpha ~ N(0,1)
## beta ~ N(1,1)
bayesian = fit(@formula(infy_log ~ nifty_log), df, LinearRegression(),Prior_Gauss(),0.0,1.0,[1.0],[1.0])


┌ Info: Found initial step size
└   ϵ = 0.025
Chains MCMC chain (1000×15×1 Array{Float64, 3}):

Iterations        = 501:1:1500
Number of chains  = 1
Samples per chain = 1000
Wall duration     = 0.64 seconds
Compute duration  = 0.64 seconds
parameters        = σ, α, β[1]
internals         = lp, n_steps, is_accept, acceptance_rate, log_density, hamiltonian_energy, hamiltonian_energy_error, max_hamiltonian_energy_error, tree_depth, numerical_error, step_size, nom_step_size

Summary Statistics
  parameters      mean       std   naive_se      mcse        ess      rhat   ess_per_sec
      Symbol   Float64   Float64    Float64   Float64    Float64   Float64       Float64

           σ    0.0330    0.0011     0.0000    0.0000   557.1259    0.9992      866.4478
           α    0.0020    0.0014     0.0000    0.0000   960.0706    0.9993     1493.1113
        β[1]    0.6671    0.0643     0.0020    0.0029   456.0534    0.9997      709.2587

Quantiles
  parameters      2.5%     25.0%     50.0%     75.0%     97.5%
      Symbol   Float64   Float64   Float64   Float64   Float64

           σ    0.0308    0.0322    0.0330    0.0337    0.0350
           α   -0.0007    0.0011    0.0020    0.0030    0.0048
        β[1]    0.5389    0.6218    0.6679    0.7123    0.7949