Anomalous volatility scaling in high frequency financial data

Volatility of intra-day stock market indices computed at various time horizons exhibits a scaling behaviour that differs from what would be expected from fractional Brownian motion (fBm). We investigate this anomalous scaling by using empirical mode decomposition (EMD), a method which separates time series into a set of cyclical components at different time-scales. By applying the EMD to fBm, we retrieve a scaling law that relates the variance of the components to a power law of the oscillating period. In contrast, when analysing 22 different stock market indices, we observe deviations from the fBm and Brownian motion scaling behaviour. We discuss and quantify these deviations, associating them to the characteristics of financial markets, with larger deviations corresponding to less developed markets.Comment: 25 pages, 11 figure, 5 table

Modified detrended fluctuation analysis based on empirical mode decomposition

Detrended fluctuation analysis (DFA) is a simple but very efficient method for investigating the power-law long-term correlations of non-stationary time series, in which a detrending step is necessary to obtain the local fluctuations at different timescales. We propose to determine the local trends through empirical mode decomposition (EMD) and perform the detrending operation by removing the EMD-based local trends, which gives an EMD-based DFA method. Similarly, we also propose a modified multifractal DFA algorithm, called an EMD-based MFDFA. The performance of the EMD-based DFA and MFDFA methods is assessed with extensive numerical experiments based on fractional Brownian motion and multiplicative cascading process. We find that the EMD-based DFA method performs better than the classic DFA method in the determination of the Hurst index when the time series is strongly anticorrelated and the EMD-based MFDFA method outperforms the traditional MFDFA method when the moment order $q$ of the detrended fluctuations is positive. We apply the EMD-based MFDFA to the one-minute data of Shanghai Stock Exchange Composite index, and the presence of multifractality is confirmed.Comment: 6 RevTex pages including 5 eps figure

Stock market returns and economic activity: evidence from wavelet analysis

In this paper we investigate the relationship between stock market returns and economic activity by using signal decomposition techniques based on wavelet analysis. In particular, we apply the maximum overlap discrete wavelet transform (MODWT) to the DJIA stock price index and the industrial production index for US over the period 1961:1- 2005:3 and using the definitions of wavelet variance, wavelet correlation and cross-correlations analyze the association as well as the lead/lag relationship between stock prices and industrial production at the different time scales. Our results show that stock market returns tends to lead the level of economic activity but only at the highest scales (lowest frequencies), corresponding to periods of 16 months and longer, and that the periods by which stock returns lead output increase as the wavelet time scale increases.stock market, industrial production, wavelet analysis

A Wavelet Analysis of MENA Stock Markets

In this paper we revisit the issue of integration of emerging stock markets with each other and with the developed markets over different time horizons using weekly stock indices data from June 1997 until March 2005 of the five major MENA equity markets (Egypt, Israel, Jordan, Morocco and Turkey) and applying the discrete wavelet decomposition analysis. We decompose the weekly stock market returns of the main indices of the MENA countries into different time scale components using the non-decimated discrete wavelet transform and then analyze the time- scale relationship between the stock market indices of some developed areas (SP and Eurostoxx) and those of the MENA countries. The results from wavelet correlation analysis both among MENA stock markets and between these markets and some major stock markets suggests that MENA stock markets are nor regionally nor internationally integrated.stock market returns, comovements, wavelet correlation analysis

Are Trump and Bitcoin Good Partners?

During times of extreme market turmoil, it is acknowledged that there is a tendency towards "flight to safety". A strong (weak) safe haven is defined as an asset that has a significant positive (negative) return in periods where another asset is in distress, while hedge has to be negatively correlated (uncorrelated) on average. The Bitcoin's surge alongside the aftermath of Trump's win in the 2016 U.S. presidential elections has strengthened its status as the modern safe haven. This paper uses a truly noise-assisted data analysis method, termed as Ensemble Empirical Mode Decomposition-based approach, to examine whether Bitcoin can act as a hedge and safe haven for U.S. stock price index. The results document that the Bitcoin's safe-haven property is time-varying and that it has primarily been a weak safe haven in the short term and the long-term. We also demonstrate that precious metals lost their safe haven properties over time as the correlation between gold/silver and U.S. stock price declines from short-to long-run horizons

The Changing Relationship Between Job Loss Announcements and Stock Prices: 1970-1999

We study the reaction of stock prices to announcements of reductions in force (RIFs) using a sample of 4273 such announcements in 1160 large firms during the 1970-99 period collected from the Wall Street Journal. We note that the total number of actual announcements for the firms in our sample follows the business cycle quite closely. We then examine changes over time in standard summary statistics (means, medians, fraction positive) of the distribution of stock market reactions, measured by the cumulative excess returns (CER) of firms’ stock prices over a 3-day event window centered on the announcement date, as well as changes over time in kernel density estimates of this distribution. We find clear evidence that the distribution of stock market reactions shifted to the right (became less negative) over time. One possible explanation for this change is that, over the last three decades, RIFs designed to improve efficiency have become more common relative to RIFs designed to cope with reductions in product demand. We estimate multivariate regression models of the CER controlling for the stated reason for the announceed layoff, industry, and other characteristics of the announced layoff. We find that almost none of the decline in the negative average stock price reaction between the 1970s and 1990s can be explained by these factors

Growth accounting for the euro area: a structural approach

This paper is concerned with the estimation of euro area potential output growth and its decomposition according to the sources of growth. The growth accounting exercise is based on a multivariate structural time series model which combines the decomposition of total output according to the production function approach with price and wage equations that embody Phillips type relationships linking inflation and nominal wage dynamics to the output gap and cyclical unemployment, respectively. Assuming a Cobb-Douglas technology with constant returns to scale, potential output results from the combination of the trend levels of total factor productivity and factor inputs, capital and labour (hours worked), which is decomposed into labour intensity (average hours worked), the employment rate, the participation rate, and population of working age. The nominal variables (prices and wages) play an essential role in defining the trend levels of the components of potential output, as the latter should pose no inflationary pressures on prices and wages. The structural model is further extended to allow for the estimation of potential output growth and the decomposition according to the sources of growth at different horizons (long-run, medium run and short run); in particular, we propose and evaluate a model–based approach to the extraction of the low–pass component of potential output growth at different cutoff frequencies. The approach has two important advantages: the signal extraction filters have an automatic adaptation property at the boundaries of the sample period, so that the real time estimates do not suffer from what is often referred to as the ”end–of-sample bias”. Secondly, it is possible to assess the uncertainty of potential output growth estimates with different degrees of smoothness. JEL Classification: C32, C51, E32, O47euro area, Low-pass filters, output gap, potential output, Production function approach, Unobserved Components

On the Co-movement of Crude, Gold Prices and Stock Index in Indian Market

This non-linear relationship in the joint time-frequency domain has been studied for the Indian National Stock Exchange (NSE) with the international Gold price and WTI Crude Price being converted from Dollar to Indian National Rupee based on that week's closing exchange rate. Though a good correlation was obtained during some period, but as a whole no such cointegration relation can be found out. Using the \textit{Discrete Wavelet Analysis}, the data was decomposed and the presence of Granger Causal relations was tested. Unfortunately no significant relationships are being found. We then studied the \textit{Wavelet Coherence} of the two pairs viz. NSE-Nifty \& Gold and NSE-Nifty \& Crude. For different frequencies, the coherence between the pairs have been studied. At lower frequencies, some relatively good coherence have been found. In this paper, we report for the first time the co-movements between Crude Oil, Gold and Indian Stock Market Index using Wavelet Analysis (both Discrete and Continuous), a technique which is most sophisticated and recent in market analysis. Thus for long term traders they can include gold and/or crude in their portfolio along with NSE-Nifty index in order to decrease the risk(volatility) of the portfolio for Indian Market. But for short term traders, it will not be effective, not to include all the three in their portfolio