Package 'MisRepARMA'

Misreported time series analysis

Description

Provides a simple and trustworthy methodology for the analysis of misreported continuous time series. See Moriña, D, Fernández-Fontelo, A, Cabaña, A, Puig P. (2021) <https://arxiv.org/abs/2003.09202v2>.

Details

Package:	MisRepARMA
Type:	Package
Version:	0.2.0
Date:	2026-04-22
License:	GPL version 2 or newer
LazyLoad:	yes

The package implements function fitMisRepARMA, which is able to fit an ARMA time series model to misreported data, and the function reconstruct which is able to reconstruct the most likely real series.

Author(s)

David Moriña, Amanda Fernández-Fontelo, Alejandra Cabaña, Pedro Puig, Biel Abarca Galván

Mantainer: David Moriña Soler <[email protected]>

References

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

Kunsch, H.R. (1989) The jackknife and the bootstrap for general stationary observations. Annals of Statistics, 17, 1217–1241.

Moriña, D., Fernández-Fontelo, A., Cabaña, A., Puig, P. (2021): New statistical model for misreported data with application to current public health challenges. arXiv preprint (https://arxiv.org/pdf/2003.09202.pdf)

Politis, D.N. and Romano, J.P. (1994) The stationary bootstrap. Journal of the American Statistical Association, 89, 1303–1313.

See Also

MisRepARMA-package, fitMisRepARMA, reconstruct

---

Fit ARMA model to misreported time series data

Description

Fits an ARMA model to misreported (underreported or overreported) continuous time series data using either a frequentist bootstrap-based EM algorithm (method = "freq") or a Bayesian MCMC approach via JAGS (method = "bayes").

Usage

fitMisRepARMA(y, tol, B, p_AR, q_MA, covars = NULL, misReport = "U",
              method = "freq", n_chains = 3, n_burnin = NULL,
              n_thin = 1, w_prior_a = 1, w_prior_b = 1, ...)

Arguments

y	numeric vector or time series of observed (potentially misreported) data.
tol	tolerance to stop the iterative EM algorithm. A value of 1e-4 is recommended.
B	for method = "freq": number of bootstrap resamples. For method = "bayes": total MCMC iterations per chain (minimum 500 recommended; 2000 or more for reliable convergence).
p_AR	non-negative integer: order of the AR part of the latent ARMA process.
q_MA	non-negative integer: order of the MA part of the latent ARMA process.
covars	optional numeric matrix of covariates to account for trends or seasonal patterns. Default is NULL.
misReport	character string: "U" (default) for underreported data ($0 < q < 1$) or "O" for overreported data ($q > 1$).
method	character string: "freq" (default) for the frequentist bootstrap-based EM approach, or "bayes" for the Bayesian MCMC approach via JAGS.
n_chains	(Bayesian only) number of parallel MCMC chains. Default is 3.
n_burnin	(Bayesian only) burn-in iterations to discard. Default is NULL (20% of B).
n_thin	(Bayesian only) thinning interval. Default is 1.
w_prior_a	(Bayesian only) first shape parameter of the Beta prior for $\omega$: $\omega \sim \mathrm{Beta}(a, b)$. Default is 1 (uniform prior).
w_prior_b	(Bayesian only) second shape parameter of the Beta prior for $\omega$. Default is 1 (uniform prior).
...	additional arguments passed to tsboot.

Details

The model assumes a latent ARMA($p$, $r$) process $X_t$ that is only partially observed through:

$Y_t = \begin{cases} X_t & \text{with probability } 1-\omega \\ q \cdot X_t & \text{with probability } \omega \end{cases}$

where $q$ is the misreporting intensity and $\omega$ is its frequency.

The frequentist method estimates parameters via an iterative EM algorithm with bootstrap uncertainty quantification.

The Bayesian method samples from the full posterior via JAGS, initialising chains near the frequentist estimates. Convergence should be checked with the Gelman-Rubin statistic ($\hat{R} < 1.1$) accessible via attr(fit, "jags")$BUGSoutput$summary.

Value

An object of class fitMisRepARMA with elements:

data	the original observed series.
t0	point estimates (EM or posterior medians). Last element is AIC (frequentist) or DIC (Bayesian).
t	matrix of bootstrap replicates or MCMC posterior samples.

Attributes: q (misreporting intensity), w (frequency), z (misreporting indicator), covars (covariate fit), x_rec (Bayesian latent process), DIC (Bayesian), jags (full JAGS object, Bayesian only).

Author(s)

David Morina, Amanda Fernandez-Fontelo, Alejandra Cabana, Pedro Puig, Biel Abarca Galvan

References

Morina, D., Fernandez-Fontelo, A., Cabana, A., Puig, P. (2021): New statistical model for misreported data with application to current public health challenges. Scientific Reports, 11, 23321. doi:10.1038/s41598-021-02620-5

See Also

MisRepARMA-package, reconstruct

Examples

set.seed(12345)
x   <- arima.sim(model = list(ar = 0.4), n = 100)
ind <- rbinom(100, 1, 0.6)
y   <- ifelse(ind == 0, x, x * 0.3)

mod_freq <- fitMisRepARMA(y, tol = 1e-4, B = 50, p_AR = 1, q_MA = 0,
                          misReport = "U", method = "freq")
summary(mod_freq)
reconstruct(mod_freq)

## Not run: 
mod_bayes <- fitMisRepARMA(y, tol = 1e-4, B = 1000, p_AR = 1, q_MA = 0,
                           misReport = "U", method = "bayes",
                           n_chains = 3, n_burnin = 200)
summary(mod_bayes)

## End(Not run)

---

Reconstruct the most likely series

Description

Reconstructs the most likely series.

Usage

reconstruct(object)

Arguments

object

object of class fitMisRepARMA.

Value

the function returns a vector of the same length of data containing the reconstruction of the most likely series.

Author(s)

David Moriña, Amanda Fernández-Fontelo, Alejandra Cabaña, Pedro Puig, Biel Abarca Galván

References

D. Moriña, A. Fernández-Fontelo, A. Cabaña, P. Puig (2021): New statistical model for misreported data with application to current public health challenges. arXiv preprint (https://arxiv.org/pdf/2003.09202.pdf)

Davison, A. C. and Hinkley, D. V. (1997) Bootstrap Methods and Their Applications. Cambridge University Press, Cambridge. ISBN 0-521-57391-2

See Also

MisRepARMA-package, fitMisRepARMA

Examples

### Example 1: frequentist reconstruction
set.seed(12345)
x   <- arima.sim(model = list(ar = 0.4), n = 100)
ind <- rbinom(100, 1, 0.6)
y   <- ifelse(ind == 0, x, x * 0.3)

fit  <- fitMisRepARMA(y, tol = 1e-6, B = 50, p_AR = 1, q_MA = 0,
                      covars = NULL, misReport = "U", method = "freq")
x_hat <- reconstruct(fit)
plot(y,     type = "l", col = "black", ylab = "Series",
     main = "Observed (black) vs reconstructed (red)")
lines(x_hat, col = "red", lty = 2)

## Not run: 
### Example 2: Bayesian reconstruction (requires R2jags and JAGS)
fit_b  <- fitMisRepARMA(y, tol = 1e-6, B = 5000, p_AR = 1, q_MA = 0,
                        covars = NULL, misReport = "U", method = "bayes",
                        n_chains = 3, n_burnin = 1000)
x_hat_b <- reconstruct(fit_b)
lines(x_hat_b, col = "blue", lty = 3)
legend("topright", legend = c("Observed", "Freq.", "Bayes"),
       col = c("black","red","blue"), lty = c(1,2,3))

## End(Not run)

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