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 2.66% per annum.
- NSC price at the close of April 27, 2022 was $262.53 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 23.45% per annum.
- NSC price at the close of April 27, 2022 was inside the secondary price channel.
- 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 NSC 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: February 12, 2021
End date: April 27, 2022
a = 5.4810
b = 0.0001
s = 0.0475
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 2.66%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0475) – 1
= 20.95%
February 12, 2021 calculations
Top border of price channel:
Exp(Y955)
= Exp(a + b × X955 + 2 × s)
= Exp(a + b × 1,386 + 2 × s)
= Exp(5.4810 + 0.0001 × 1,386 + 2 × 0.0475)
= Exp(5.6758)
= $291.73
Bottom border of price channel:
Exp(Y955)
= Exp(a + b × X955 – 2 × s)
= Exp(a + b × 1,386 – 2 × s)
= Exp(5.4810 + 0.0001 × 1,386 – 2 × 0.0475)
= Exp(5.4857)
= $241.21
April 27, 2022 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(5.4810 + 0.0001 × 1,825 + 2 × 0.0475)
= Exp(5.7074)
= $301.10
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(5.4810 + 0.0001 × 1,825 – 2 × 0.0475)
= Exp(5.5173)
= $248.96
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 2.66% per annum.
- NSC price at the close of April 27, 2022 was $262.53 and was inside the primary price channel.
Secondary Trend
Start date: December 6, 2021
End date: April 27, 2022
a = 6.9015
b = -0.0007
s = 0.0310
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -23.45%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0310) – 1
= 13.20%
December 6, 2021 calculations
Top border of price channel:
Exp(Y1,160)
= Exp(a + b × X1,160 + 2 × s)
= Exp(a + b × 1,683 + 2 × s)
= Exp(6.9015 + -0.0007 × 1,683 + 2 × 0.0310)
= Exp(5.7314)
= $308.39
Bottom border of price channel:
Exp(Y1,160)
= Exp(a + b × X1,160 – 2 × s)
= Exp(a + b × 1,683 – 2 × s)
= Exp(6.9015 + -0.0007 × 1,683 – 2 × 0.0310)
= Exp(5.6074)
= $272.43
April 27, 2022 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(6.9015 + -0.0007 × 1,825 + 2 × 0.0310)
= Exp(5.6274)
= $277.94
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(6.9015 + -0.0007 × 1,825 – 2 × 0.0310)
= Exp(5.5034)
= $245.53
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 23.45% per annum.
- NSC price at the close of April 27, 2022 was inside the secondary price channel.
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