Average True Range 真实波动幅度均值

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Average True Range 真实波动幅度均值

来自：MACD论坛(bbs.macd.cn) 作者：lyaaa 浏览：32863 回复：5

Average True Range is an indespensable tool for designers of good trading systems. It is truly a workhorse among technical indicators. Every systems trader should be familiar with ATR and its many useful functions. It has numerous applications including use in setups, entries, stops and profit taking. It is even a valuable aid in money management.
　　
　　真实波动幅度均值（ATR）是优秀的交易系统设计者的一个不可缺少的工具，它称得上是技术指标中的一匹真正的劲马。每一位系统交易者都应当熟悉ATR及其具有的许多有用功能。其众多应用包括：参数设置，入市，止损，获利等，甚至是资金管理中的一个非常有价值的辅助工具。
　　
　　译者注：setups在上篇文章中我也碰到，我把它翻译为参数设置，不知道对不对。
　　
　　The following is a brief explanation of how ATR is calculated and a few simple examples of the many ways that ATR can be used to design profitable trading systems.
　　
　　ATR是如何计算的？下面我们会简单解释的；如何利用ART设计交易系统？我们随后也会用几个简单例子说明众多方法中的一些。
　　
　　How to calculate Average True Range (ATR).
　　
　　如何计算真实波动幅度均值（ATR）
　　
　　Range: This is simply the difference between the high point and the low point of any bar.
　　True Range: This is the GREATEST of the following:
　　1. The distance from today\'s high to today\'s low
　　2. The distance from yesterday\'s close to today\'s high, or
　　3. The distance from yesterday\'s close to today\'s low
　　True range is different from range whenever there is a gap in prices from one bar to the next.
　　Average True Range is simply the true range averaged over a number of bars of data.
　　
　　波动幅度：单根K线图最高点和最低点间的距离。（译者将原文用的是条形图改为我们熟悉的K线图）
　　
　　真实波动幅度：是以下三个波动幅度的最大值
　　
　　1. 当天最高点和最低点间的距离
　　2. 前一天收盘价和当天最高价间的距离，或
　　3. 前天收盘价和当天最低价间的距离
　　
　　当日K线图出现缺口时，真实波动幅度和单根K线的波动幅度是不同的。
　　
　　真实波动幅度均值就是真实波动幅度的平均值
　　
　　To make ATR adaptive to recent changes in volatility, use a short average (2 to 10 bars). To make the ATR reflective of \"normal\" volatility use 20 to 50 bars or more.
　　
　　为了让ATR反映近期波动性，可以使用短期ATR（2－10根K线图）；为了让ATR反映“长期”波动性，可以使用20至50根K线或更多。
　　
　　Characteristics and benefits of ATR.
　　
　　ATR的特征及其益处
　　
　　ATR is a truly adaptive and universal measure of market price movement.
　　Here is an example that might help illustrate the importance of these characteristics:
　　
　　ATR是一个评价市场价格运动的通用指标，而且是一个真正的自适应指标。
　　下面这个例子能帮助解释这些特征的重要性
　　
　　If we were to measure the average price movement of Corn over a two day period and express this in dollars it might be a figure of about $500.00. If we were to measure the average price movement of a Yen contract it would probably be about $2,000 or more. If we were building a system where we wanted to use the set appropriate stop losses in Corn and Yen we would be looking at two very different stop levels because of the difference in the volatility (in dollars). We might want to use a $750 stop loss in Corn and a $3,000 stop loss in Yen. If we were building one system that would be applied identically to both of these markets it would be very difficult to have one stop expressed in dollars that would be applicable to both markets. The $750 Corn stop would be too close when trading Yen and the $3,000 Yen stop would be too far away when trading Corn.
　　
　　如果我们计算一下玉米在两天内的平均价格波动幅度，比如说是500美元；日元合约的平均价格波动幅度可能是2,000美元或更多。如果我们要建立一个交易系统分别为玉米或日元设置合适的止损水平，那么我们会看到这两者的止损水平是不同的，因为两者的波动性不同。我们可能在玉米上设定750美元的止损水平，而在日元合约上是3,000美元。如果我们要建立一个能同时适用于这两个市场的交易系统，我们很难在这两个市场上让用美元数量表示的止损水平相等。750美元的止损水平对玉米来说是合适的，但对日元来说可能太小了；3,000美元的止损水平对日元来说是合适的，但对玉米来说太大了。
　　
　　However, let\'s assume that, using the information in the example above, the ATR of Corn over a two day period is $500 and the ATR of Yen over the same period is $2,000. If we were to use a stop expressed as 1.5 ATRs we could use the same formula for both markets. The Corn stop would be $750 and the Yen stop would be $3,000.
　　
　　然而，我们不妨假定在上面的例子中，玉米在两天内的真实波动幅度均值（ATR）是500美元，日元在两天内的真实波动幅度均值（ATR）是2,000美元。如果我们把止损水平设置为1.5倍的ATR（即用ATR表示的止损水平），我们就能在这两个市场使用相同的标准（即1.5倍的ATR），玉米的止损水平会是750美元，日元的止损水平会是3000美元。
　　
　　Now lets assume that the market conditions change so that Corn becomes extremely volatile and moves $1,000 over a two day period and Yen gets very quiet and now moves only $1,000 over a two day period. If we were still using our stops as originally expressed in dollars we would still have a $750 stop in Corn (much too close now) and a $3,000 stop in Yen (much too far away now). However, our stop expressed in units of ATR would adapt to the changes and our new ATR stops of 1.5 ATRs would automatically change our stops to $1500 for Corn and $1500 for Yen. The ATR stops would automatically adjust to the changes in the market without any change in the original formula. Our new stop is 1.5 ATRs the same as always.
　　
　　现在让我们假定市场条件变了，玉米波动性变的很高，两天之内运动了1000美元；而日元变得很平静，两天之内只运动了1000美元。如果我们还使用以前的用美元数量表示的止损水平，即玉米的止损水平仍然定为750美元，日元的止损水平仍然定为3000美元，那么现在玉米的止损水平定的太近了，而日元的止损水平又定得太远了。然而，用ATR的某一倍数表示的止损水平能适应市场的变化，1.5倍ATR的止损水平将自动调整玉米和日元的止损水平分别为1500美元。用ATR表示的止损水平能自动适应市场的变化，同时不会改变原先的止损标准，新情况下的止损标准与以前的止损标准一样，同是1.5倍ATR。
　　
　　The value of having ATR as a universal and adaptive measure of market volatility can not be overstated. ATR is an invaluable tool in building systems that are robust (this means they are likely to work in the future) and that can be applied to many markets without modification. Using ATR you might be able to build a system for Corn that might actually work in Yen without the slightest modification. But perhaps more importantly, you can build a system using ATR that works well in Corn over your historical data and that is also likely to work just as well in the future even if the nature of the Corn data changes dramatically.
　　
　　ATR作为市场波动性指标具有的通用性和适应性的使用价值无论怎么肯定都不过分。ATR对于建立坚实的交易系统是非常有价值的（也就是说交易系统可能在未来同样有效），而且他们能不加修饰的用于多个市场。使用ATR你可以设计一个既适用于玉米市场，同样也可以在没有任何修改的情况下用于日元市场。但是，或许更重要的是，你可以建立一个系统，它不仅在玉米的历史数据测试中表现良好，它同样也很有可能在未来即使玉米市场变化很大的情况下仍然表现良好。
　　
　　Sample Applications of ATR as an entry tool:
　　
　　ATR作为一种入场工具的应用示例
　　
　　Entry Setups: (Remember, entry setups tell us when a possible trade is near.
　　
　　Entry triggers tell us to do the trade now.)
　　
　　入场背景：（记住，入场背景告诉我们不久将会出现交易机会，而入场触发器告诉我们现在入场交易）
　　
　　Range contraction setup: Many technicians have observed that big moves often emerge from quiet sideways markets. These quiet periods can be detected quite easily by comparing a short period ATR with a longer period ATR. For example if the 10 bar ATR is only .75 or less of the 50 period ATR it would indicate that the market has been unusually quiet lately. This can be a setup condition that tells us an important entry is near.
　　
　　波动区间收缩背景：许多技术派已经注意到大幅价格运动往往出现在价格平静的横盘整理之后。通过比较短期ATR和长期ATR可以非常容易的鉴别出价格平静的横盘整理区间，比如当10期ATR小于等于0.75倍50期ATR时，就表明近期市场不寻常的平静。这就是一个背景条件，表明关键的入场时机就在眼前。
　　
　　Range expansion setup: Many technicians believe that unusually high volatility means that a sustainable trend is underway. Range expansion periods are just the opposite of the range contraction periods. Range expansion periods can be measured by requiring that the 10 bar ATR be some amount greater than the 50 period ATR. For example the 10 bar ATR must be 1.25 or more times the 50 period ATR.
　　
　　波动区间扩张背景：许多技术派相信不同寻常的价格移动意味着一个幅度可观的趋势正在形成。波动区间扩张时期正好与波动区间收缩时期相反，这时我们要求10期ATR大于50期ATR，例如10期ATR大于等于50期ATR的1.25倍。
　　
　　If you are concerned about the apparent contradiction of these two theories we could easily combine them. We could require that a period of low volatility be followed by a period of unusually high volatility before looking for our entry.
　　
　　如果你对这两种截然相反的情况有兴趣，我们可以非常容易的将两者融合在一起。我们寻找的入场机会在什么时候呢？在波动区间收缩之后紧跟着波动区间扩张的时候。
　　
　　Dip or rally setup: Lets assume that we want to buy a market only after a dip or sell it only after a rally. We could tell our system to prepare for a buy entry whenever the price is 3 ATRs or more lower than it was five days ago. Our setup to sell on a rally would be that we want to sell short only when the price is 3 ATRs or more higher than it was five days ago. The choice of 3 ATRs and five days is simply an example and isn抰 necessarily a recommended choice of parameters. You will have to figure out the proper parameters on your own depending on the unique requirements of your particular system.
　　
　　回调或反弹背静：假定我们只想在市场回调时买入，在市场反弹时卖出。当价格比5天前的价格至少低3倍ATR时，我们可以让我们的系统准备买入。当价格比5天前的价格至少高出3倍ATR时，我们可以让我们的交易系统准备卖空。
　　
　　Entry Triggers:
　　
　　入场触发器：
　　
　　Volatility Breakout: This theory assumes that a sudden large move in one direction indicates that a trend in the direction of the breakout has begun. Normally the entry rule goes something like this: Buy on a stop if the price rises 2 ATRs from yesterday抯 close. Or sell short on a stop if the price declines 2 ATRs from the previous close. The general concept here is that on a normal day the price will only rise or fall 1 ATR or less from the previous close. Rising or falling 2 ATRs is an unusual occurrence and indicates that something out of the ordinary has influenced the prices to cause the breakout. The inference is that whatever caused this breakout has major importance and a new trend is beginning.
　　
　　波动性突变：该理论认为突然出现的某个方向的大幅运动表明与该方向相同的趋势正在形成。一般来说，我们的入场规则可以表述为：当价格比上一交易日收盘价高2ATR时买入，当价格比上一交易日收盘价低2ATR时卖出。这里的一般概念是在平常交易日里价格涨跌不会超过上一交易日收盘价1ATR，超过上一交易日收盘价2ATR的价格涨跌是不寻常的事件，这表明有什么不同寻常的事发生了。由此可以做出的结论是：促使价格这么运动的原因是实质性的，一个新的趋势正在形成。
　　
　　Some volatility systems operate by measuring the breakout in points rather than units of ATR. For example the system may require that the Yen must rise 250 points from the previous close to signal a breakout to the upside. Systems measuring points rather than units of ATR may need frequent reoptimization to stay in tune with current market conditions. However, breakouts measured in units of ATR should not require reoptimization because, as we previously explained, the ATR value contracts and expands with changing market conditions.
　　
　　一些波动性突变系统的评价标准以点数为单位，而不是以ATR为单位。例如它们认为当日元比上一个收盘价高出250点时才表明上升趋势出现。以点数为单位而不是以ATR为单位的交易系统需要不断的调整优化，才能与市场变化保持一致。然而，以ATR为单位的交易系统不需要优化，正如我们以前解释的那样，ATR值会随着市场变化而变化。
　　
　　Change in direction trigger: Lets assume that we want to buy a dip in a rising market. We combine the dip or rally setup described above with an entry trigger that tells us the dip or rally may be over and the primary trend is resuming.
　　
　　方向改变触发器：假定我们想在上升趋势中的回调买入，我们可以将我们之前谈到的回调或反弹背景与入场触发器结合起来，后者能告诉我们什么时候回调或反弹已经结束，也就是告诉我们主要趋势什么时候正在恢复。
　　
　　The series of rules might read something like this: If the close today is 2.0 ATRs greater than the 40 day moving average (this condition establishes that the long term trend is still up) and the close today is 2 ATRs or more below the close seven days ago (this condition establishes that we are presently in a dip within the uptrend) then buy tomorrow if the price rises 0.8 ATRs above todays low. This entry trigger shows that we have rallied significantly from a recent low and that the dip is probably over. As we enter the trade the prices are again moving in the direction of the major trend.
　　
　　这一系列规则可以表述为：如果今天的收盘价比40天移动均价高2ATR或更多，这表明长期趋势是向上的；而且今天的收盘价比七天前的收盘价低2ATR或更多，这表明我们正处在上升趋势的回调中，那么我们就会在明天价格比今天最低价高出0.8ATR时买入。入场触发器表明市场已经从近期低点中恢复上涨，回调可能已经结束，当我们进入市场后，市场会再次向主趋势方向运动。
　　
　　As you can see, the ATR can be a most valuable tool for designing logical entries. In our next article we will discuss using ATR in our exit strategies and give some interesting examples.
　　
　　正如你在上面看到的，ATR在设计合理入场策略时是非常有价值的工具。在我们的下篇文章中，我们将会讨论ATR在退出策略中的应用，并给出一些有趣的应用实例。
　　
　　Using Average True Range for Exits
　　
　　ATR在离市中的应用
　　
　　In this Bulletin we will show how ATR can help us achieve more accurateexits.
　　
　　在本文中我们将向大家展示ATR如何帮助我们更准确的离市
　　
　　ATR EXIT TARGETS: Perhaps the most valuable of all application of ATR is to use it to define profit objectives. If we were to run some tests to define profit objective in terms of dollars we could probably find a particular dollar amount that produced acceptable results when reviewing historical data. Just as an example, let\'s assume that we run some optimizations to find the best level at which to take profits in a particular market and we find that the best number is $1250. Although this amount may produce acceptable results on a historical basis it is not always the best solution to the problem.
　　
　　ATR出场策略：或许ATR最有价值的应用是用来确定盈利目标。如果我们对用美元数量表示的盈利目标进行测试，我们很可能找到这样一个美元数量表示的盈利目标，它在历史数据测试中能产生理想的回报。比如，假设我们经过优化后已经找到能在某一特定市场获得正期望收益的最佳盈利目标——1250美元。虽然该方法能在历史测试中获得满意效果，但这不是解决问题的最好方法。
　　
　　When the market is quiet and there is little volatility our profits are likely to fall well short of our $1250 objective. However when the market is volatile and trending strongly our potential profit might be much greater than $1250. The $1250 level is simply a not so happy medium that is usually either too large a target or too small a target.
　　
　　当市场平静的时，波动性变小，我们的盈利极可能低于1250美元的目标；然而当市场波动性变大，而且形成一个强劲的趋势，我们的潜在盈利很可能远大于1250美元。1250美元的目标水平无法让人满意，要么有时目标水平太高，要么有时目标水平太低。
　　
　　On the other hand if we measure our profit objective in terms of ATR we have a much more robust and logical solution. Lets assume that we run our tests again looking for units of ATR instead of dollars. Assume our research shows us that our best profit objective is now expressed as 4 ATRs. In a normal market 4 ATRs might be equal to $1250, the same as our dollar denominated target. However in a quiet market 4 ATRS might only be $800. The advantage of our ATR research is that while our original $1250 target is no longer obtainable because of the quiet market conditions the ATR target has adapted to the change in volatility and can still be achieved.
　　
　　相反，如果我们用ATR来限定我们的盈利目标，我们将会找到一个更强健更合理的解决方法。让我们用ATR代替美元作为盈利目标单位，重新进行测试，测试结果表明最佳盈利目标是4ATR。在正常情况下，4ATR的盈利目标就等于1250美元的盈利目标；然而在市场平静时，4ATR可能仅等于800美元。ATR作为盈利目标单位的优点在于：当市场变平静时，原来1250美元的盈利目标无法实现，而ATR能随着波动性的改变而改变，因而原来的4ATR盈利目标还能实现。
　　
　　Increases in volatility produce an even more dramatic effect. Let\'s assume that the market is suddenly streaking in one direction because of some important news. Our 4 ATRs is now $5,000. Wouldn抰 it be a shame if our system was taking profits of $1250 when the market is willing to give us $5,000 or more.
　　
　　波动性增加能带来更大的影响。比如某一重要的新闻使市场突然向某一方向飞跑，我们4ATR的目标现在相当于5000美元，所以当市场能给我们5000美元或更多的时候，我们却把盈利目标定为1250美元，这样的交易系统难道不会让我们很没面子吗？
　　
　　streak Vi 快速移动，飞跑；Vt使布满条纹
　　
　　n 条纹，纹理；（of）个性特征［倾向］；一段时期
　　
　　In addition to setting profit objectives, ATR can also be very helpful in placing trailing stops. Here are two examples that you may recall from discussions on the FORUM page and past BULLETINS.
　　
　　除了帮我们设定盈利目标，ATR还能帮助我们设置跟踪止损点。这里我们举两个例子，或许你会记得我们以前在论坛和通讯里面讨论过。
　　
　　THE CHANDELIER EXIT: We have often advocated the importance of good exits and this is one of our favorites. The exit stop is placed at a multiple of average true ranges from the highest high or highest close since the entry of the trade. As the highs get higher the stop moves up but it never moves downward.
　　
　　吊灯止损法：我们常常强调一个好的离市在交易中的重要性，我们喜欢这么强调。我们把止损点放在离我们入市后的最高点或最高收盘价某一ATR处，随着高点越变越高，我们的止损点也逐渐上移，而不是下移。
　　
　　chandelier 枝形吊灯
　　
　　Examples:
　　
　　示例：
　　
　　Exit at the highest high since entry minus 3 ATR on a stop.
　　
　　止损点放在自我们入市交易后的最高价减去3ATR处。
　　
　　Exit at the highest close since entry minus 2.5 ATR on a stop.
　　
　　止损点放在自我们入市交易后的最高收盘价减去2.5ATR处。
　　
　　Application: We like the Chandelier Exit as one of our exits for trend following systems. (The name is derived from the fact that the exit is hung downward from the ceiling of a market.)
　　
　　应用：我们喜欢把吊灯止损法应用于趋势跟踪系统。（我们这么命名，是因为我们注意到该止损点很象是从市场的天花板上挂下来的。
　　
　　This exit is extremely effective at letting profits run in the direction of a trend while still offering some protection against a major reversal in trend. In fact our research has shown that this exit is so effective that you can enter futures markets at random and if you use this exit the results over time will be profitable. (If you don\'t believe us just try it.) When used for long term trend following the best values for the ATR in most markets ranges somewhere between 2.5 and 4.0.
　　
　　该止损法非常有利于让我们的盈利往趋势方向累积，同时还能保护我们免受趋势大幅反转的伤害。事实上，我们的研究表明该止损法是如此神奇有效以至于你可以随机进入期货市场，然后使用该止损法，长期来说其结果是盈利的（如果不信，可以试试看）。在长期趋势跟踪系统中，对大多数市场来说，最佳ATR值在2.5至4.0间。
　　
　　THE YO YO EXIT: This exit is very similar to the Chandelier Exit except that the ATR stop is always pegged to the most recent close instead of the highest high. Since the closes move higher and lower, the stop also moves up and down (hence the Yo Yo name). Although this stop appears similar to the Chandelier Exit the logic is quite a bit different. The Yo Yo Exit is a classic volatility stop that is intended to recognize an abnormal adverse price fluctuation that occurs in one day. This abnormal volatility is often the result of a news event or some important technical reversal that is likely to signal the end of a trend. This logic makes the YO YO exit very effective and we seldom regret being stopped out whenever this exit is triggered.
　　
　　YO YO止损法：该法非常类似于吊灯止损法，差别仅在于其ATR止损点总是盯牢上一个收盘价的，而不是盯牢最高价（或最高收盘价）。由于上一个收盘价不断的变高或变底，止损点也跟着上移或下移（因为我们把它叫做YO YO止损法）。尽管两种止损法表面上很像，但其逻辑还是相当有区别的。YO YO止损法是典型的波动性止损法，即用于辨别一个交易日内异常的不利的价格波动。这种异常波动往往是由于某一新闻事件，或是一种重要的技术性反转（是趋势结束的标志）。这种逻辑使得YO YO止损法非常有效，我们很少因为这种止损触发的退出交易而后悔。
　　
　　We should caution you that the Yo Yo stop should never be our only loss protection because if the price moves slowly against our position the Yo Yo stop also moves away each day and, in theory, the stop may never be hit.
　　
　　我们必须提醒你YO YO止损法绝不是我们唯一的亏损保护措施，因为如果价格是缓慢的向不利于我们仓位的方向移动，YO YO止损点也跟着一天天的往下移，永远也不会触发止损点，这在理论上是可能的。
　　
　　Combining the exits: The Yo Yo and the Chandelier exits work best when used together. The Chandelier Exit is typically set at 3 ATRs or more from a high point and never lowered; therefore it will protect us against any gradual reversal of trend. The Yo Yo exit is typically set at only 1.5 to 2.0 ATRs from the most recent close and will protect our position from unusual one day spikes in volatility. When used together the operative stop each day would be whichever of the two stops is closest.
　　
　　综合两种止损方法：综合使用YO YO止损法和吊灯止损法更有效。吊灯止损点往往设在距离最高点（或最高收盘价）3ATR或更多的地方，在市场向不利于我们的方向移动时，该止损点是不变的，因此他将保护我们免受趋势逐渐逆转的伤害。YO YO止损点往往设在离上一个收盘价仅1.5或2ATR处，它可以保护我们免受异常的日内价格的剧烈波动。当两者同时使用时，每天的止损价会是两者中最先被触发的那个。
　　
　　spike n 尖状物；曲线上的陡升线。
　　
　　Money Management Advice: When using any stops based on multiples of ATR we should keep in mind that volatility can quickly expand to where our risk is greater than we intended. We do not want to unknowingly exceed the risk limitations dictated by our money management scheme so we should also have a \"worst case\" dollar based stop available or be prepared to reduce our position size quickly as the ATR values expand. When should we reduce our position size and when should we implement our fixed dollar stop?
　　
　　资金管理建议：当使用任何一种基于ATR的止损点，我们必须记住波动性可以很快大到使我们承受得风险比我们计划要承受的大。我不想在不知不觉中超过资金管理限定的风险水平，因此我们必须有一个“在最坏情况下的”基于美元单位的止损水平，或者我们必须在ATR变大时迅速减少我们的头寸。什么时候我们该减少我们的头寸规模？什么时候该实行我们的固定的美元止损点？两者该如何取舍？
　　
　　If we are on the right side of the volatility expansion it may not be wise to reduce our position size just as the trade is beginning to do what we hoped for. For this reason I prefer to implement the dollar based stop on profitable positions rather than reducing the size of winning positions prematurely. We obviously want to have big positions in our winners and small positions in our losers. Therefore it would make sense to reduce our position size only if the volatility is increasing in a trade that is going against us. Once extremely large profits have been achieved, positions can safely be reduced without sacrificing too much in the way of potential profits.
　　
　　如果波动性扩张时我们在正确的方向，减少持仓规模是不明智的，因为市场正向我们希望的方向发展。基于这个原因，在有盈利潜能的仓位上我倾向于采用基于美元的止损点而不是采用过早的减少盈利仓位的规模。显然，我们想在盈利时持有大仓位，在损失时持有小仓位。因此在市场向不利于我们的方向发展，且波动性变大时，减少我们的头寸规模才是明智的。一旦获得巨大的盈利，仓位可以被安全的减少而不会牺牲太多的潜在赢利。
　　
　　By now we hope you have begun to appreciate the value of ATR in designing systems. There are still more uses for ATR that we have yet to discuss (Keltner Bands for example). We hope to have additional articles about ATR sometime in the future. In the meantime we hope this series of articles has stimulated some creative thinking about the many uses of ATR. Lets us know if you come up with more creative ideas on how to apply this wonderful technical tool.
　　
　　文章写到现在，我们希望你已经开始肯定ATR在交易系统设计中的作用。还有很多ATR用法有待讨论（比如Keltne带）。我们希望将来还能写一些关于ATR的文章，我们还希望这一系列文章能激起一些关于ATR用法的创造性想法。如果你有的话，请告诉我们你是如何创造性的应用这一伟大的技术分析工具。

naiti

楼主辛苦了

jeff_yuan

:*19*:

istudying

谢谢楼主的提供，学习了。

jinghao262

*d:1* :*19*: