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 263.99% per annum.
- APA price at the close of August 4, 2016 was $50.18 and was lower than the bottom border of the primary price channel by $15.87 (24.02%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 5.85% per annum.
- APA price at the close of August 4, 2016 was lower than the bottom border of the secondary price channel by $0.06 (0.12%).
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 APA 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 6, 2016
End date: June 8, 2016
a = -2.1501
b = 0.0035
s = 0.0615
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0035) – 1
= 263.99%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0615) – 1
= 27.87%
January 6, 2016 calculations
Top border of price channel:
Exp(Y1,111)
= Exp(a + b × X1,111 + 2 × s)
= Exp(a + b × 1,615 + 2 × s)
= Exp(-2.1501 + 0.0035 × 1,615 + 2 × 0.0615)
= Exp(3.6894)
= $40.02
Bottom border of price channel:
Exp(Y1,111)
= Exp(a + b × X1,111 – 2 × s)
= Exp(a + b × 1,615 – 2 × s)
= Exp(-2.1501 + 0.0035 × 1,615 – 2 × 0.0615)
= Exp(3.4435)
= $31.30
June 8, 2016 calculations
Top border of price channel:
Exp(Y1,217)
= Exp(a + b × X1,217 + 2 × s)
= Exp(a + b × 1,769 + 2 × s)
= Exp(-2.1501 + 0.0035 × 1,769 + 2 × 0.0615)
= Exp(4.2345)
= $69.02
Bottom border of price channel:
Exp(Y1,217)
= Exp(a + b × X1,217 – 2 × s)
= Exp(a + b × 1,769 – 2 × s)
= Exp(-2.1501 + 0.0035 × 1,769 – 2 × 0.0615)
= Exp(3.9886)
= $53.98
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 263.99% per annum.
- APA price at the close of August 4, 2016 was $50.18 and was lower than the bottom border of the primary price channel by $15.87 (24.02%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: April 12, 2016
End date: August 4, 2016
a = 4.2940
b = -0.0002
s = 0.0378
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -5.85%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0378) – 1
= 16.33%
April 12, 2016 calculations
Top border of price channel:
Exp(Y1,177)
= Exp(a + b × X1,177 + 2 × s)
= Exp(a + b × 1,712 + 2 × s)
= Exp(4.2940 + -0.0002 × 1,712 + 2 × 0.0378)
= Exp(4.0869)
= $59.56
Bottom border of price channel:
Exp(Y1,177)
= Exp(a + b × X1,177 – 2 × s)
= Exp(a + b × 1,712 – 2 × s)
= Exp(4.2940 + -0.0002 × 1,712 – 2 × 0.0378)
= Exp(3.9357)
= $51.20
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(4.2940 + -0.0002 × 1,826 + 2 × 0.0378)
= Exp(4.0681)
= $58.45
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.2940 + -0.0002 × 1,826 – 2 × 0.0378)
= Exp(3.9168)
= $50.24
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 5.85% per annum.
- APA price at the close of August 4, 2016 was lower than the bottom border of the secondary price channel by $0.06 (0.12%).
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