Time-varying Multiplier Research Articles

Angle Tracking Adaptive Backstepping Control for a Mechanism of Pneumatic Muscle Actuators via an AESO

This paper presents an adaptive backstepping controller for a mechanism of pneumatic muscle actuators via an adaptive extended state observer. A dynamic model of the mechanism is established with two unknown parameters estimated by using adaptive laws. An adaptive extended state observer is established to estimate total disturbances and states of the mechanism. Moreover, adaptive extended state observer gains are obtained by adaptive laws and parallel D-eigenvalues, whose time-varying multiplier $n$ th-order derivatives are derived by tracking differentiators. Finally, a nonlinear adaptive backstepping controller is designed and the effectiveness of the proposed method is expressed by experimental results.

Time variation in the size of the multiplier: a Kalecki–Harrod approach

A growing empirical literature demonstrates that the size of the expenditure multiplier varies over time, being both larger and consistently greater than one during periods of slow growth and/or recession. This paper contributes to the theory of the time-varying multiplier. It is shown that a combination of Kalecki's dynamic theory of investment and Harrod's ‘satisficing’ approach to the investment decision furnish a theory in which the ‘crowding in’ of investment expenditures following an initial demand stimulus gives rise to an elevated expenditure multiplier during times of pronounced macroeconomic distress.

Time Variation in the Size of the Multiplier: A Kalecki-Harrod Approach

A growing empirical literature demonstrates that the size of the expenditure multiplier varies over time, being both larger and consistently greater than one during periods of slow growth and/or recession. This paper contributes to the theory of the time-varying multiplier. It is shown that a combination of Kalecki’s dynamic theory of investment and Harrod’s “satisficing” approach to the investment decision furnish a theory in which the “crowding in” of investment expenditures following an initial demand stimulus (fiscal or otherwise) gives rise to an elevated expenditure multiplier during times of pronounced macroeconomic distress.

Performance evaluation of optimized portfolio insurance strategies

We use S&P 500 index return data for the time period 1985–2013 to evaluate the performance of portfolio insurance strategies. We shed light on the question if the performance of a constant proportion portfolio insurance (CPPI) strategy can be improved by means of a time-varying multiplier which depends on the estimated future volatility. Neglecting any inter-temporal hedging demand, the theoretical foundation of the strategies is given by maximizing the expected utility of a HARA investor in a diffusion model setup. If the risk premium is assumed to be proportional to the variance, the optimal strategy is a CPPI strategy. Otherwise, the multiple is time-varying (PPI). It turns out that even time-varying multiple strategies based on a rolling window of historical volatility estimates give a significant improvement of CPPI strategies. The out-performance is robust w.r.t. alternative performance measures and is also true for proportional transaction costs and adequate trigger trading.

Performance Evaluation of Optimized Portfolio Insurance Strategies

We use S&P 500 index return data for the time period 1985-2012 to evaluate the performance of portfolio insurance strategies. We shed light on the question if the performance of a constant proportion portfolio insurance (CPPI) strategy can be improved by means of a time-varying multiplier which depends on the estimated future volatility. Neglecting any inter-temporal hedging demand, the theoretical foundation of the strategies is given by maximizing the expected utility of a HARA investor in a diffusion model setup. If the risk premium is assumed to be proportional to the variance, the optimal strategy is a CPPI strategy. Otherwise, the multiple is time-varying (PPI). It turns out that even time-varying multiple strategies based on a rolling window of historical volatility estimates give a significant improvement of CPPI strategies. The out-performance is robust w.r.t. alternative performance measures and is also true for proportional transaction costs and adequate trigger trading.

Reconstruction of Nonuniformly Sampled Bandlimited Signals Using a Differentiator–Multiplier Cascade

This paper considers the problem of reconstructing a bandlimited signal from its nonuniform samples. Based on a discrete-time equivalent model for nonuniform sampling, we propose the differentiator-multiplier cascade, a multistage reconstruction system that recovers the uniform samples from the nonuniform samples. Rather than using optimally designed reconstruction filters, the system improves the reconstruction performance by cascading stages of linear-phase finite impulse response (FIR) filters and time-varying multipliers. Because the FIR filters are designed as differentiators, the system works for the general nonuniform sampling case and is not limited to periodic nonuniform sampling. To evaluate the reconstruction performance for a sinusoidal input signal, we derive the signal-to-noise-ratio at the output of each stage for the two-periodic and the general nonuniform sampling case. The main advantage of the system is that once the differentiators have been designed, they are implemented with fixed multipliers, and only some general multipliers have to be adapted when the sampling pattern changes; this reduces implementation costs substantially, especially in an application like time-interleaved analog-to-digital converters (TI-ADCs) where the timing mismatches among the ADCs may change during operation.

Reconstruction of Two-Periodic Nonuniformly Sampled Band-Limited Signals Using a Discrete-Time Differentiator and a Time-Varying Multiplier

This brief considers the problem of reconstructing a band-limited signal from its two-periodic nonuniformly spaced samples. We propose a novel reconstruction system where a finite-impulse response filter designed as differentiator followed by a time-varying multiplier recovers the uniformly spaced from the nonuniformly spaced samples. The system roughly doubles the signal-to-noise ratio with relatively few filter coefficients. The main advantage is that once the differentiator has been designed, it can be implemented with fixed multipliers, and only the coefficients of the time-varying multiplier have to be adapted when the sampling pattern changes; this reduces implementation costs substantially. In addition, the system allows an efficient polyphase implementation.

A simple form synthesis of linear time-variant digital filter via spectral decomposition of its impulse response

The paper describes a new technique to synthesize a finite impulse response of linear time-variant (LTV) digital filter. First, a finite impulse response is decomposed into a sum of products of two orthogonal sequences. The direct implementation of the decomposed impulse response leads to the parallel connection of linear time-invariant (LTI) digital filters, followed by time-varying multipliers. A simple filter structure is obtained by properly modifying the sequences to realize the parallel form structure as a cascade connection of first- or second-order recursive LTI filters. The structure is easy to implement on a computer and saves computation time. Numerical examples illustrating the technique are included.