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 58.34% per annum.
- IBM price at the close of May 16, 2024 was $168.97 and was lower than the bottom border of the primary price channel by $8.87 (4.99%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 44.33% per annum.
- IBM price at the close of May 16, 2024 was lower than the bottom border of the secondary price channel by $1.36 (0.80%).
- 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 IBM 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: March 7, 2023
End date: April 24, 2024
a = 2.9703
b = 0.0013
s = 0.0443
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 58.34%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0443) – 1
= 19.39%
March 7, 2023 calculations
Top border of price channel:
Exp(Y957)
= Exp(a + b × X957 + 2 × s)
= Exp(a + b × 1,390 + 2 × s)
= Exp(2.9703 + 0.0013 × 1,390 + 2 × 0.0443)
= Exp(4.8091)
= $122.62
Bottom border of price channel:
Exp(Y957)
= Exp(a + b × X957 – 2 × s)
= Exp(a + b × 1,390 – 2 × s)
= Exp(2.9703 + 0.0013 × 1,390 – 2 × 0.0443)
= Exp(4.6319)
= $102.71
April 24, 2024 calculations
Top border of price channel:
Exp(Y1,242)
= Exp(a + b × X1,242 + 2 × s)
= Exp(a + b × 1,804 + 2 × s)
= Exp(2.9703 + 0.0013 × 1,804 + 2 × 0.0443)
= Exp(5.3304)
= $206.51
Bottom border of price channel:
Exp(Y1,242)
= Exp(a + b × X1,242 – 2 × s)
= Exp(a + b × 1,804 – 2 × s)
= Exp(2.9703 + 0.0013 × 1,804 – 2 × 0.0443)
= Exp(5.1532)
= $172.98
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 58.34% per annum.
- IBM price at the close of May 16, 2024 was $168.97 and was lower than the bottom border of the primary price channel by $8.87 (4.99%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: March 6, 2024
End date: April 24, 2024
a = 8.0880
b = -0.0016
s = 0.0099
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0016) – 1
= -44.33%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0099) – 1
= 4.04%
March 6, 2024 calculations
Top border of price channel:
Exp(Y1,208)
= Exp(a + b × X1,208 + 2 × s)
= Exp(a + b × 1,755 + 2 × s)
= Exp(8.0880 + -0.0016 × 1,755 + 2 × 0.0099)
= Exp(5.2913)
= $198.60
Bottom border of price channel:
Exp(Y1,208)
= Exp(a + b × X1,208 – 2 × s)
= Exp(a + b × 1,755 – 2 × s)
= Exp(8.0880 + -0.0016 × 1,755 – 2 × 0.0099)
= Exp(5.2517)
= $190.89
April 24, 2024 calculations
Top border of price channel:
Exp(Y1,242)
= Exp(a + b × X1,242 + 2 × s)
= Exp(a + b × 1,804 + 2 × s)
= Exp(8.0880 + -0.0016 × 1,804 + 2 × 0.0099)
= Exp(5.2126)
= $183.58
Bottom border of price channel:
Exp(Y1,242)
= Exp(a + b × X1,242 – 2 × s)
= Exp(a + b × 1,804 – 2 × s)
= Exp(8.0880 + -0.0016 × 1,804 – 2 × 0.0099)
= Exp(5.1731)
= $176.46
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 44.33% per annum.
- IBM price at the close of May 16, 2024 was lower than the bottom border of the secondary price channel by $1.36 (0.80%).
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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