# Ds lppl bubble indicator forex

- Eur/usd analysis forexprostr
- 2 Окт, 2012
- 5

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There is no clear evidence whether others were indeed crashes followed by a bubble period. Additionally, a change of regime is signaled quite earlier in a few other cases. The rest of the paper is organized as follows. Section 3 presents the findings. The final section concludes the paper. JLS consider a risk neutral rational agent with rational expectations.

This implies an asset price p t following a martingale process. In market equilibrium, there is equality between asset price and its conditional expectation given all information available up to time t. This is a necessary condition for no arbitrage.

As it is well- known, the hazard rate gives the probability of a crash in the next time period given that it has not occurred yet. See Seyrich and Sornette for a recent micro-foundation. The susceptibility quantifies the degree of sensitivity of a system to external perturbation. It is the probability that a group of agents will have the same state given externals influences in the network. In real financial markets, interacting investors are organized inside a hierarchical network, where people locally influence each other at many different levels.

Derrida et al. It is similar to the rational imitation model in a random or regular network with one difference. Within this mechanism, the behavior of the crash hazard rate is similar to that of susceptibility in the neighborhood of the critical crash point. These parameters are further described in Sornette and Johansen and Johansen This equation is given in various forms in several papers: Sornette b , Lin et al.

For both developed and emerging stock markets, Johansen et al. First, a faster than exponential or super-exponential growth of the stock price during the bubble period, which ends when the bubble fades. Second, oscillations with an accelerating frequency that can be represented as approximately in geometrical proportional to the distance to the critical time tc the most probable time for a regime change or end of bubble.

The parameter tc is the most probable time for a change in the regime at which the growth rate changes, signifying a change in regime. The regime change may be the time of the crash, the burst of the bubble, or the fading of the bubble. Not all bubbles end with a crash and therefore the change in regime is not necessarily a crash. The regime change, however, will be a change from super-exponential growth to a lower growth and the end of the accelerating oscillations.

Therefore, this component is the power law singular component. It is the component that embodies the positive feedback mechanism of a bubble development. The sign requirements on B arise from the condition that prices should rise during a positive bubble and fall during a negative bubble.

In order to overcome to complexity of the minimization, metaheuristic algorithms such as the taboo search or genetic algorithm is used to estimate the parameters of the LPPL model. Filimonov and Sornette proposed transforming the LLPLS equation 5 in order to reduce the number of nonlinear parameters from 4 to 3 at the expense of increasing the number of linear parameters from 3 to 4.

The transformation substantially reduces the complexity of the fitting procedure and improves its stability, allowing the simple algorithms, such as the Gauss- Newton algorithm, to be used efficiently. The transformed function is characterized by better smooth properties and in general by a single or a few minima. Data and Empirical Results 3. Data come from the Global Financial Database. We define two targets for our investigation: positive bubbles and negative bubbles.

To illustrate why the concept of negative bubble is useful, consider the case when the CHF in Euro is exhibiting a positive bubble. Then, by construction, the Euro in CHF follows a negative bubble. The notion of a positive bubble or bubble in the standard definition assumes that the numeraire the value of reference in which the price is expressed has no ambiguity. Usually, it is taken as being the US dollar. However, this does not need to be the case and stressing the value of reference provides novel insights.

Negative bubbles are interesting for the study of arbitrary pairs of assets where one asset is expressed in units of the other. Another way to express the same thing is to consider a self-financing portfolio that is long the first asset and short the second asset.

All the analyses are causal, i. In the figures, we tag the periods of positive resp. The red marks diagnose positive bubbles, associated with upward accelerating prices, which are susceptible to regime change in the form of crashes or volatile sideway plateaus. The green marks diagnose negative bubbles, associated with downward accelerating prices, which are susceptible to change of regimes in the form of rallies or volatile sideway plateaus.

One can observe that bubbles are identified quite early, but the signals often do not stop immediately as the real bubbles fade. The status of those periods that remain blank white is no bubble. The marked periods do not all correspond to bubbles or negative bubbles. Although some of these events are classified as known bubbles, there is no clear evidence on the status of the others.

These events are listed in Table 1 along with some others that are classified as bubble. We next examine the existence of bubbles in these periods using robust indicators. Table 1. It was followed by a 3. After then, Six Year sharp decline in these prices. The panic had the bubble burst and the both domestic and foreign origins, such as index fell to 2. The and made a trough in subsequent recession made profits, prices, at 1. The cumulative and wages to go down and unemployment to decline from June to raise.

On September 20, , September The Panic of The U. However, overproduction against a Thereafter, the declining market, deflation , and the index started to fall until depression in Europe triggered a depression , following a negative that lasted from until It is also bubble. Confidence value: 0. The panic was caused by two bank 5. Street Crash falling prices in some agricultural products Thereafter, the bubble burst of 10 and heavy emigration from rural to urban are and the index made a trough listed as the causes of the great depression.

It started in Hong Kong The crash Internet-based companies experienced fast following the end of bubble growth during the period of — The bubble collapsed October March to Following, the end of the bubble the reaching The default rates on subprime and adjustable-rate market then entered a mortgages ARM increased quickly. The financial crisis of fell to The crisis later value: 0. At any time t, we fit the LPPLS model with the historic data and check the quality of the calibrations.

A fit must pass a strict Lomb log- periodic test Zhou and Sornette, , unit-root test of the residuals Lin and Sornette, , and other criteria explained and justified in Johansen and Sornette, ; Sornette et al. A very low value indicates risk of over-fitting since the signal is only observed in one or two specific windows. In this case, the result needs to be considered with care. The End-of- Bubble signals of positive bubbles, however, are able to predict a large fraction 11 Johansen and Sornette , developed a methodology to characterize drawdowns drawups robustly.

Drawdowns drawups were simply defined as a continuous decrease increase in the value of the price, while allowing for small noise decorating the main trend. A drawdown drawup is terminated by a sufficiently large increase decrease in the price.

Drawdowns drawups are thus robust cumulative losses gains from the last local maximum minimum to the next minimum maximum. All these are positive bubble cases. The positive bubbles signals correspond to following events: the Panic of , the Panic of the Black Friday , the Panic of , the Panic of , the Wall Street Crash of , the Black Monday of , the Dot-com bubble of , and the Subprime Financial Crises of Although other events have been well- documented as bubbles before and have been studied using bubble detection methodologies, to the best of our knowledge, the evidence for bubble presented here for the Panic of , the Panic of , and the Panic of is novel.

Therefore, our present study presents for the first time solid statistical evidence of bubbles for these cases. Thus, the bubble confidence for the Panic of is considerably high. The Panic of is signaled as early as , the Panic of as early as , the Crash of as early as , and the Black Monday of as early as However, the signal comes relatively late and weak for the Subprime Mortgage Crises of Therefore, the negative bubbles also corresponds to known well- documented events..

There are, however, three bubble signals in , , for which there are no recorded events for these periods. But one can observe clear change of regimes following the peak of these signals, suggesting value for mitigating market risks when using such indicators.

Comparison with other methods In this section, we use two additional bubble identification methods in order to compare the results obtained from the DS LPPLS methodology. In this way, we can both compare the results and do a robustness check by using these alternative methods.

Two methods we use for confirmatory and comparative analysis are the exponential curve fitting EXCF method of Watanabe et al. The EXCF is based on the idea that an exponential growth curve fits better than a linear model to bubble periods. The EXCF method determines a data based window size to date-stamp the bubbles and crashes automatically. The window size is determined such that exponential growth would not be observed when an exponential curve is fitted to the data covering a sample size larger than this minimum window size.

Balcilar et al. Once the minimum window size is determined, a rolling estimation procedure is used to determine the bubble periods. The GSADF is a recursive right-tailed unit root testing procedure that allows the identification of multiple periods of price explosiveness. Here, following the suggestions of Phillips et al. This method uses a flexible moving sample test procedure to consistently and efficiently detect and date-stamp periods where a price series displays a root exceeding unity.

Phillips et al. We first comment on the results from the EXCF model. The EXCF procedure identifies 14 bubble periods over the whole sample period. Among the 14 bubble periods, five corresponds to historically known and documented events as bubbles or crashes. The GSADF test identifies 10 bubble periods, five of these corresponding to known and documented events, one as an early signal for the panic of as early as , and four false signals.

Table 2. Four bubbles, the Panic of , the Panic of , the Wall Street Crash of , and the Dot- com bubble of , are identified jointly by all three methods. The DS LPPLS system also identifies previously unclassified bubble regimes, which are clearly associated with significant changes of regimes, providing additional value for a global riks management perspective.

Overall, the DS LPPLS system accurately identifies more of the historically events that are known as bubbles and has fever or no false signals if one recognizes the value of the regime-switching identification. The distinguishing feature of this study from the previous studies is that this paper is the first of its kind that examines the existence of bubbles in the US stock prices using two hundreds years of monthly data with an advanced bubble detection methodology based on the LPPLS model.

We showed that each of these bubble periods correspond to well-known and well-documented historical events, implying that the detection algorithm indeed accurately detect the bubbles. To the best of our knowledge, three of the bubble periods, the Panic of , the Panic of , and the Panic of , that our methodology detects correspond to well-known events, but not studied in the literature using bubble detection methodologies.

Two negative bubbles detected by our methodology do also correspond to known events. Thus the bubble indicators for these events are also correct signals. Our study shows that, among the 19 events documented as bear market, crash, or the bubble in the history of the US stock market between and , only eight events can be classified as positive bubbles with positive feedback mechanism.

Additionally two events are classified as negative bubbles. These bubbles and crashes in the stock market, triggered by various reasons, all developed a positive or negative in two cases feedback mechanism, a self-perpetuating pattern of investment behavior. The positive negative feedback mechanism translates into super-exponential growth decline in stock prices.

However, not all stock market crashed or crises are caused by internal bubble mechanisms with positive negative feedback mechanism. Section 6 describes a method to alternate the solution of the non-linear least-square problem with the solution of a linear sub-system while ensuring the exact computation of the Jacobian. Section 7 describes the evaluation methodology and reports on the evaluation results. Section 8 concludes the paper. The importance of recency can be increased by taking smaller values of W.

Returning to the case of general weights, recency can be progressively emphasized by decreasing weights more rapidly for progressively older data points. Recency weighting is relatively less important during the last stages of a bubble. When a bubble is approaching its critical time T, recent prices are much larger than older prices. Thus, the least-square objective is affected more by recent data points than older ones. However, recency weighting is important when the bubble is in its early stages because price values are relatively close to each other.

The existence of local minima can be partly obviated by starting LMA from multiple initial solutions. Initial solutions can be selected via Taboo search [ 10 ]. Yet, in the presence of a strong LPPL component to price data, initial solutions can also be chosen by inspection of the price series. In this paper, the initial solutions are determined as follows.

In other words, the exponential starting point can be interpreted informally as testing for the null hypothesis that prices grow exponentially, i. For example, two consecutive peaks of the LPPL function are consecutive in angle points j and k in Fig.

An estimate i, j, and k is obtained by selecting three consecutive price peaks or troughs. It is an open question to automate the selection of i,j,k, for example, with a visual pattern recognition algorithm. The LMA process will be started from multiple initial parameters.

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