Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 103.97% per annum.
- BAX price at the close of August 4, 2016 was $48.08 and was lower than the bottom border of the primary price channel by $2.97 (5.82%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 50.50% per annum.
- BAX price at the close of August 4, 2016 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of BAX price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: January 4, 2016
End date: May 18, 2016
a = 0.4061
b = 0.0020
s = 0.0197
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0020) – 1
= 103.97%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0197) – 1
= 8.19%
January 4, 2016 calculations
Top border of price channel:
Exp(Y1,109)
= Exp(a + b × X1,109 + 2 × s)
= Exp(a + b × 1,613 + 2 × s)
= Exp(0.4061 + 0.0020 × 1,613 + 2 × 0.0197)
= Exp(3.5956)
= $36.44
Bottom border of price channel:
Exp(Y1,109)
= Exp(a + b × X1,109 – 2 × s)
= Exp(a + b × 1,613 – 2 × s)
= Exp(0.4061 + 0.0020 × 1,613 – 2 × 0.0197)
= Exp(3.5169)
= $33.68
May 18, 2016 calculations
Top border of price channel:
Exp(Y1,203)
= Exp(a + b × X1,203 + 2 × s)
= Exp(a + b × 1,748 + 2 × s)
= Exp(0.4061 + 0.0020 × 1,748 + 2 × 0.0197)
= Exp(3.8593)
= $47.43
Bottom border of price channel:
Exp(Y1,203)
= Exp(a + b × X1,203 – 2 × s)
= Exp(a + b × 1,748 – 2 × s)
= Exp(0.4061 + 0.0020 × 1,748 – 2 × 0.0197)
= Exp(3.7805)
= $43.84
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 103.97% per annum.
- BAX price at the close of August 4, 2016 was $48.08 and was lower than the bottom border of the primary price channel by $2.97 (5.82%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: February 24, 2016
End date: August 4, 2016
a = 1.8201
b = 0.0011
s = 0.0235
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 50.50%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0235) – 1
= 9.84%
February 24, 2016 calculations
Top border of price channel:
Exp(Y1,144)
= Exp(a + b × X1,144 + 2 × s)
= Exp(a + b × 1,664 + 2 × s)
= Exp(1.8201 + 0.0011 × 1,664 + 2 × 0.0235)
= Exp(3.7306)
= $41.70
Bottom border of price channel:
Exp(Y1,144)
= Exp(a + b × X1,144 – 2 × s)
= Exp(a + b × 1,664 – 2 × s)
= Exp(1.8201 + 0.0011 × 1,664 – 2 × 0.0235)
= Exp(3.6367)
= $37.97
August 4, 2016 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(1.8201 + 0.0011 × 1,826 + 2 × 0.0235)
= Exp(3.9120)
= $50.00
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.8201 + 0.0011 × 1,826 – 2 × 0.0235)
= Exp(3.8181)
= $45.52
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 50.50% per annum.
- BAX price at the close of August 4, 2016 was inside the secondary price channel.
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