pad_tau function

Pad and unpad changepoint sets with boundary points

pad_tau(tau, n)

unpad_tau(padded_tau)

is_valid_tau(tau, n)

regions_tau(tau, n)

validate_tau(tau, n)

Arguments

• tau: a numeric vector of changepoint indices
• n: the length of the original time series
• padded_tau: Output from pad_tau()

Returns

• pad_tau(): an integer vector that starts with 0 and ends in $n$.

• unpad_tau(): an integer vector stripped of its first and last entries.

• is_valid_tau(): a logical if all of the entries are between 2 and $n-1$.

• regions_tau(): A base::factor()

• validate_tau(): an integer vector with only the base::unique()

  entries between 2 and $n-1$, inclusive.

Details

If a time series contains $n$ observations, we label them from 1 to $n$. Neither the 1st point nor the $n$th point can be a changepoint, since the regions they create on one side would be empty. However, for dividing the time series into non-empty segments, we start with 1, add $n+1$, and then divide the half-open interval $[1, n+1)$ into half-open subintervals that define the regions.

pad_tau() ensures that 1 and $n+1$ are included.

unpad_tau() removes 1 and $n+1$, should they exist.

is_valid_tau() checks to see if the supplied set of changepoints is valid

validate_tau() removes duplicates and boundary values.

Examples

# Anything less than 2 is not allowed
is_valid_tau(0, length(DataCPSim))
is_valid_tau(1, length(DataCPSim))

# Duplicates are allowed
is_valid_tau(c(42, 42), length(DataCPSim))
is_valid_tau(826, length(DataCPSim))

# Anything greater than \eqn{n} (in this case 1096) is not allowed
is_valid_tau(1096, length(DataCPSim))
is_valid_tau(1097, length(DataCPSim))

# Always return a factor with half-open intervals on the right
regions_tau(c(42, 330), 1096)
# Anything less than 2 is not allowed
validate_tau(0, length(DataCPSim))
validate_tau(1, length(DataCPSim))
validate_tau(826, length(DataCPSim))

# Duplicates are removed
validate_tau(c(826, 826), length(DataCPSim))

# Anything greater than \eqn{n} (in this case 1096) is not allowed
validate_tau(1096, length(DataCPSim))
validate_tau(1097, length(DataCPSim))

# Fix many problems
validate_tau(c(-4, 0, 1, 4, 5, 5, 824, 1096, 1097, 182384), length(DataCPSim))