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 21.59% per annum.
- ITW price at the close of February 11, 2022 was $217.72 and was lower than the bottom border of the primary price channel by $4.44 (2.00%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 5.79% per annum.
- ITW price at the close of February 11, 2022 was lower than the bottom border of the secondary price channel by $1.43 (0.65%). This indicates a possible reversal in the secondary trend direction.
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 ITW 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: October 9, 2018
End date: February 3, 2022
a = 4.5470
b = 0.0005
s = 0.0601
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 21.59%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0601) – 1
= 27.20%
October 9, 2018 calculations
Top border of price channel:
Exp(Y417)
= Exp(a + b × X417 + 2 × s)
= Exp(a + b × 603 + 2 × s)
= Exp(4.5470 + 0.0005 × 603 + 2 × 0.0601)
= Exp(4.9902)
= $146.96
Bottom border of price channel:
Exp(Y417)
= Exp(a + b × X417 – 2 × s)
= Exp(a + b × 603 – 2 × s)
= Exp(4.5470 + 0.0005 × 603 – 2 × 0.0601)
= Exp(4.7496)
= $115.54
February 3, 2022 calculations
Top border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 + 2 × s)
= Exp(a + b × 1,816 + 2 × s)
= Exp(4.5470 + 0.0005 × 1,816 + 2 × 0.0601)
= Exp(5.6397)
= $281.39
Bottom border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 – 2 × s)
= Exp(a + b × 1,816 – 2 × s)
= Exp(4.5470 + 0.0005 × 1,816 – 2 × 0.0601)
= Exp(5.3991)
= $221.21
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 21.59% per annum.
- ITW price at the close of February 11, 2022 was $217.72 and was lower than the bottom border of the primary price channel by $4.44 (2.00%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: March 15, 2021
End date: February 11, 2022
a = 5.1797
b = 0.0002
s = 0.0356
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 5.79%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0356) – 1
= 15.30%
March 15, 2021 calculations
Top border of price channel:
Exp(Y1,027)
= Exp(a + b × X1,027 + 2 × s)
= Exp(a + b × 1,491 + 2 × s)
= Exp(5.1797 + 0.0002 × 1,491 + 2 × 0.0356)
= Exp(5.4808)
= $240.03
Bottom border of price channel:
Exp(Y1,027)
= Exp(a + b × X1,027 – 2 × s)
= Exp(a + b × 1,491 – 2 × s)
= Exp(5.1797 + 0.0002 × 1,491 – 2 × 0.0356)
= Exp(5.3384)
= $208.18
February 11, 2022 calculations
Top border of price channel:
Exp(Y1,259)
= Exp(a + b × X1,259 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(5.1797 + 0.0002 × 1,824 + 2 × 0.0356)
= Exp(5.5321)
= $252.68
Bottom border of price channel:
Exp(Y1,259)
= Exp(a + b × X1,259 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.1797 + 0.0002 × 1,824 – 2 × 0.0356)
= Exp(5.3897)
= $219.15
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 5.79% per annum.
- ITW price at the close of February 11, 2022 was lower than the bottom border of the secondary price channel by $1.43 (0.65%). This indicates a possible reversal in the secondary trend direction.
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