SMC (version 1.0)

auxiliaryParticleFilter: The auxiliary particle filtering algorithm

Description

Function for doing auxiliary particle filtering given the state equation (via generateNextStreamsFunc), the stream representative generation rule (via generateStreamRepsFunc), and the observation equation density (via logObsDensFunc).

Usage

auxiliaryParticleFilter(nStreams,                          
                        nPeriods,                          
                        dimPerPeriod,                      
                        generateStreamRepsFunc,            
                        generateNextStreamsFunc,            
                        logObsDensFunc,                    
                        resampCriterionFunc = NULL,  
                        resampFunc          = NULL, 
                        summaryFunc         = NULL,  
                        nMHSteps            = 0,     
                        MHUpdateFunc        = NULL,  
                        nStreamsPreResamp   = NULL,  
                        returnStreams       = FALSE, 
                        returnLogWeights    = FALSE, 
                        verboseLevel        = 0,     
                        ...)

Arguments

nStreams

integer $>$ 0.

nPeriods

integer $>$ 0.

dimPerPeriod

integer $>$ 0.

generateStreamRepsFunc

function of five arguments (currentPeriod, lag1Streams, lag1LogWeights, streamIndices, ...).

generateNextStreamsFunc

function of seven arguments (currentPeriod, lag1Streams, lag1LogWeights, streamIndices, streamReps, startingStreams, ...).

logObsDensFunc

function of three arguments (currentPeriod, currentStreams, ...).

resampCriterionFunc

function of four arguments (currentPeriod, currentStreams, currentLogWeights, ...).

resampFunc

function of four arguments (currentPeriod, currentStreams, currentLogWeights, ...).

summaryFunc

function of four arguments (currentPeriod, currentStreams, currentLogWeights, ...).

nMHSteps

integer $\ge$ 0.

MHUpdateFunc

function of six arguments (currentPeriod, nMHSteps, currentStreams, lag1Streams, lag1LogWeights, ...).

nStreamsPreResamp

integer $>$ 0.

returnStreams

logical.

returnLogWeights

logical.

verboseLevel

integer, a value $\ge$ 2 produces a lot of output.

...

optional arguments to be passed to generateStreamRepsFunc, generateNextStreamsFunc, logObsDensFunc, resampCriterionFunc, resampFunc, summaryFunc and MHUpdateFu

Value

• This function returns a list with the following components:
• draws
  a list with the following components: summary, propUniqueStreamIds, streams, logWeights, acceptanceRates. See the section Note for more details.
• nStreams
  the nStreams argument.
• nPeriods
  the nPeriods argument.
• dimPerPeriod
  the dimPerPeriod argument.
• nStreamsPreResamp
  the nStreamsPreResamp argument.
• nMHSteps
  the nMHSteps argument.
• filterType
  type of the filter: auxiliaryParticleFilter.
• time
  the time taken by the run.

Warning

Using very small values ($\le$ 1e3) for nStreams might not give reliable results.

Details

We introduce the following terms, which will be used in the sections Required Function and Optional Function below:

[object Object],[object Object]

References

Michael K. Pitt and Meil Shephard (1999). Filtering via Simulation: Auxiloary Particle Filters. Journal of the American Statistical Association 94(446): 590-599.

See Also

particleFilter

Examples

MSObj  <- MarkovSwitchingFuncGenerator(-2468)
smcObj <-
    with(MSObj,
     {
         auxiliaryParticleFilter(nStreams                = 5000,
                                 nPeriods                = nrow(yy),
                                 dimPerPeriod            = ncol(yy),
                                 generateStreamRepsFunc  = generateStreamRepsFunc,
                                 generateNextStreamsFunc = generateNextStreamsFunc,
                                 logObsDensFunc          = logObsDensFunc,
                                 returnStreams           = TRUE,
                                 returnLogWeights        = TRUE,
                                 verboseLevel            = 1)
     })
print(smcObj)
print(names(smcObj))
with(c(smcObj, MSObj),
 {
     par(mfcol = c(2, 1))
     plot(as.ts(yy),
          main     = expression('The data and the underlying regimes'),
          cex.main = 0.8,
          xlab     = 'period',
          ylab     = 'data and the regime means',
          cex.lab  = 0.8)
     lines(as.ts(mu), col = 2, lty = 2)
     plot(as.ts(draws$summary[1, ]),
          main     = expression('The underlying regimes and their estimates'),
          cex.main = 0.8,
          xlab     = 'period',
          ylab     = 'regime means',
          cex.lab  = 0.8)
     lines(as.ts(mu), col = 2, lty = 2)        
 })

MSObj  <- MarkovSwitchingFuncGenerator(-8642)
smcObj <-
    with(MSObj,
     {
         auxiliaryParticleFilter(nStreams                = 5000,
                                 nPeriods                = nrow(yy),
                                 dimPerPeriod            = ncol(yy),
                                 generateStreamRepsFunc  = generateStreamRepsFunc,
                                 generateNextStreamsFunc = generateNextStreamsFunc,
                                 logObsDensFunc          = logObsDensFunc,
                                 returnStreams           = TRUE,
                                 returnLogWeights        = TRUE,
                                 verboseLevel            = 1)
     })
print(smcObj)
print(names(smcObj))
with(c(smcObj, MSObj),
 {
     par(mfcol = c(2, 1))
     plot(as.ts(yy),
          main     = expression('The data and the underlying regimes'),
          cex.main = 0.8,
          xlab     = 'period',
          ylab     = 'data and the regime means',
          cex.lab  = 0.8)
     lines(as.ts(mu), col = 2, lty = 2)
     plot(as.ts(draws$summary[1, ]),
          main     = expression('The underlying regimes and their estimates'),
          cex.main = 0.8,
          xlab     = 'period',
          ylab     = 'regime means',
          cex.lab  = 0.8)
     lines(as.ts(mu), col = 2, lty = 2)        
 })